C H A P T E R S 1 – 9 CUMULATIVE REVIEW

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838

Reaction time

Braking distance

Reaction time

Braking distance

1.USED CARS The following ad appeared in The Car Trader. (O.B.O. means “or best offer.”) If offers of $8,750, $8,875, $8,900, $8,850, $8,800, $7,995, $8,995, and $8,925 were received, what was the selling price of the car? [Section 1.1]

1969 Ford Mustang. New tires Must sell!!!! $10,500 O.B.O.

2.Round 2,109,567 to the nearest thousand. [Section 1.1]

3.Add: 458 8,099 23,419 58 [Section 1.2]

4.Subtract: 35,021 23,999 [Section 1.3]

5.PARKING The length of a rectangular parking lot is 204 feet and its width is 97 feet. [Section 1.4]

a.Find the perimeter of the lot.

b.Find the area of the lot.

6.Divide: 1,363 41 [Section 1.5]

7.PAINTING One gallon of paint covers 350 square feet. How many gallons are needed if the total area of walls and ceilings to be painted is 8,400 square feet, and if two coats must be applied? [Section 1.6]

8.a. Prime factor 220. [Section 1.7]

b.Find all the factors of 12. [Section 1.7]

9.a. Find the LCM of 16 and 24. [Section 1.8]

b.Find the GCF of 16 and 24.

(3 5)2 2

10. Evaluate:		[Section 1.9]
	5)
2(8

11.a. Write the set of integers. [Section 2.1] b. Simplify: ( 3) [Section 2.1]

12.Perform the operations.

a.16 4 [Section 2.2]

b.16 ( 4) [Section 2.3]

c.16(4) [Section 2.4]

d.4 [Section 2.5]

e.42 [Section 2.4]

f.( 4)2 [Section 2.4]

13.OVERDRAFT PROTECTION A student forgot that she had only $30 in her bank account and wrote

acheck for $55 and used her debit card to buy $75 worth of groceries. On each of the two transactions, the bank charged her a $20 overdraft protection fee. Find the new account balance. [Section 2.3]

14. Evaluate: 10 4 06 ( 3)2 0 [Section 2.6]

15.a. Simplify: 3528 [Section 3.1]

b.Write 38 as an equivalent fraction with denominator 48. [Section 3.1]

c. What is the reciprocal of 8 ? [Section 3.3]

d. Write 7 12 as an improper fraction. [Section 3.5]

16.GRAVITY Objects on the moon weigh only onesixth as much as on Earth. If a rock weighs 54 ounces on the Earth, how much does it weigh on the moon?

[Section 3.2]

Perform the operations.

5			33	b [Section 3.2]
17.		a
	77		50

15 45

18.16 8 [Section 3.3]

19.4 5 [Section 3.4]

20.256 a2 247 b [Section 3.5]


	2			4
21.	45			96			[Section 3.6]
21.	45	3		96		5	[Section 3.6]
	7			2
22.	7			3	[Section 3.7]
22.	4		5		[Section 3.7]
			5

			6
23.	PET MEDICATION A pet owner was told to use an
	eye dropper to administer medication to his sick
	kitten. The cup shown below contains 8 doses of the
	medication. Determine the size of a single dose.

[Section 3.3]

1 oz

3/4 oz

1/2 oz

1/4 oz

24.BAKING A bag of all-purpose ﬂour contains 1712 cups. A baker uses 334 cups. How many cups of ﬂour are left? [Section 3.6]

25. Evaluate: 34 a 13b a54b [Section 3.7]

26. a. Round the number pi to the nearest ten thousandth: p 3.141592654. . . . [Section 4.1]

b. Place the proper symbol ( or ) in the blank: 154.34 154.33999. [Section 4.1]

c. Write 6,510,345.798 in words. [Section 4.1]

d. Write 7,498.6461 in expanded notation. [Section 4.1]

Chapter 9 Cumulative Review

839

Perform the operations.

27. 3.4 106.78 35 0.008 [Section 4.2]

28.	5,091.5 1,287.89 [Section 4.2]
29.	8.8 ( 7.3 9.5)															[Section 4.2]
30.	5.5( 3.1) [Section 4.3]
31.	0.0742						[Section 4.4]
31.			1.4				[Section 4.4]
			1.4
32.	7	(9.7 15.8) [Section 4.5]
32.	8	(9.7 15.8) [Section 4.5]
33.	PAYCHECKS If you are paid every other week,
	your monthly gross income is your gross income
	from one paycheck times 2.17. Find the monthly
	gross income of a secretary who earns $1,250 every
	two weeks. [Section 4.3]
34.	Perform each operation in your head.
	a.		(89.9708)(10,000)													[Sections 4.3]
	b.		89.9708									[Sections 4.4]

			100
			100
	Estimate the quotient: 9.2																				[Section 4.4]
35.	Estimate the quotient: 9.2																			18,460.76	[Section 4.4]
36.	Evaluate								( 1.3)2 6.7									and round the result to the
36.	Evaluate							0.9										and round the result to the
								0.9
	nearest hundredth. [Section 4.4]
			2
37.	Write							as a decimal. Use an overbar. [Section 4.5]
37.	Write					15		as a decimal. Use an overbar. [Section 4.5]
38.	Evaluate each expression. [Section 4.6]
	a.		21							31
	a.		21				121			31					64

			49
	b.			B
	b.			B	81
39.	Graph each number on the number line. [Section 4.6]
				e 4				5			, 1			2.89,			2		, 0.1, 1				3	f
								5					17,				2					9,	3
								8					17,									9,	2
								8								3							2

−5 −4 −3 −2 −1 0 1 2 3 4 5

840Chapter 9 Cumulative Review

40.Write each phrase as a ratio (fraction) in simplest form. [Section 5.1]

a.3 centimeters to 7 centimeters

b.13 weeks to 1 year

41.COMPARISON SHOPPING A dry-erase whiteboard with an area of 400 in.2 sells for $24. A larger board, with an area of 600 in.2, sells for $42. Which board is the better buy? [Section 5.1]

42.Solve the proportion: 14x 1328 [Section 5.2]

43.INSURANCE CLAIMS In one year, an auto insurance company had 3 complaints per 1,000 policies. If a total of 375 complaints were ﬁled that year, how many policies did the company have?

[Section 5.2]

44.SCALE DRAWINGS On the scale drawing below,

14 -inch represents an actual length of 3 feet. The length of the house on the drawing is 614 inches. What is the actual length of the house? [Section 5.2]

BEDROOM		BEDROOM		LIVING	DINING
BEDROOM		BEDROOM
			CLO
CLO	CLO	HALL
	CLO

					KITCHEN
STUDY		BATH	CLO	ENTRY	UTILITY
			CLO

Scale – in. : 3 ft

45.Make each conversion. [Section 5.3]

a.Convert 168 inches to feet.

b.Convert 212 ounces to pounds.

c.Convert 30 gallons to quarts.

d.Convert 12.5 hours to minutes.

46.Make each conversion. [Section 5.4]

a.Convert 1.538 kilograms to grams

b.Convert 500 milliliters to liters.

c.Convert 0.3 centimeters to kilometers.

47.THE AMAZON The Amazon River enters the Atlantic Ocean through a broad estuary, roughly estimated at 240,000 m in width. Convert the width to kilometers. [Section 5.4]

48.OCEAN LINERS When it was making cruises from England to America, the Queen Mary got 13 feet to the gallon. [Section 5.5]

a.How many meters a gallon is this?

b.The fuel capacity of the ship was 3,000,000 gallons. How many liters is this?

49.COOKING What is the weight of a 10-pound ham in kilograms? [Section 5.5]

50.Convert 75°C to degrees Fahrenheit. [Section 5.5]

51.Complete the table. [Section 6.1]

	Percent	Decimal	Fraction
	57%
		0.001
			1
			3
52.	Refer to the ﬁgure on the
	right. [Section 6.1]
	a. What percent of the ﬁgure
	is shaded?
	b. What percent is not
	shaded?
53.	What number is 15% of 450? [Section 6.2]
54.	24.6 is 20.5% of what number? [Section 6.2]
55.	51 is what percent of 60? [Section 6.2]
56.	CLOTHING SALES Find the amount of the
	discount and the sale price of the coat shown below.
	[Section 6.3]

Men’s Open Range Coat

Save Regularly 25%$820 00

Winter Coats

on Sale!

Genuine leather

57.SALES TAX If the sales tax rate is 614%, how much sales tax will be added to the price of a new car

selling for $18,550? [Section 6.3]

58.COLLECTIBLES A porcelain ﬁgurine, which was originally purchased for $125, was sold by a collector ten years later for $750. What was the percent increase in the value of the ﬁgurine? [Section 6.3]

59.TIPPING Estimate a 15% tip on a dinner that cost $135.88. [Section 6.4]

60.PAYING OFF LOANS To pay for tuition, a college student borrows $1,500 for six months. If the annual interest rate is 9%, how much will the student have to repay when the loan comes due? [Section 6.5]

61.FREEWAYS Refer to the pictograph below to answer the following questions. [Section 7.1]

Freeway Traffic

Average number of vehicles daily

I-405 Los Angeles

I-5 Seattle

I-95 New York

I-94 Minneapolis	= 50,000 vehicles
Source: www.skyscraperpage.com

a.Estimate the number of vehicles that travel the I-405 Freeway in Los Angles each day.

b.Estimate the number of vehicles that travel the I-95 Freeway in New York each day.

c.Estimate how many more vehicles travel the I-5 Freeway in Seattle than the I-94 Freeway in Minneapolis each day.

62.VEGETARIANS The graph below gives the results of a recent study by Vegetarian Times. [Section 7.1]

Survey Results: Ages of Adult

Vegetarians in the United States, 2008

Over 55 yrs old

40%	42%
35–54 yrs	18–34 yrs
old	old

Chapter 9 Cumulative Review

841

a.According to the study, what percent of the adult vegetarians in the United States are over 55 years old?

b.The study estimated that there were 7,300,000 adult vegetarians in the United States. How many of them are 35 to 54 years old?

63.SPENDING ON PETS Refer to the bar graph below to answer the following questions. [Section 7.1]

a.In what category was the most money spent on pets? Estimate how much.

b.Estimate how much money was spent on purchasing pets.

c.Estimate how much more money was spent on vet care than on grooming and boarding.

Amount Spent on Pets in the U.S., 2009

	18
	16
of dollars	14
	12
	10
Billions	10
	8
	6
	6
	4
	2
	Vet	Grooming/	Supplies/	Food	Animal
	care	boarding	medicine		purchases

Source: American Pet Products Organization

64.TABLE TENNIS The weights (in ounces) of 8 pingpong balls that are to be used in a tournament are as follows: 0.85, 0.87, 0.88, 0.88, 0.85, 0.86, 0.84, and 0.85. Find the mean, median, and mode of the weights.

[Section 7.2]

2x 3y

65. Evaluate the expression z y for x 2, y 3, and z 4. [Section 8.1]

66.Translate each phrase to an algebraic expression.

[Section 8.1]

a.16 less than twice x

b.the product of 75 and s, increased by 6

67.Simplify each expression. [Section 8.2]

a. 12(4a)

b. 2b( 7)(3)

Source: Vegetarian Times

842Chapter 9 Cumulative Review

68.Multiply. [Section 8.2]

a.9(3t 10)

b.8(4x 5y 1)

69.Combine like terms. [Section 8.2]

a.10x 7x

b.c2 4c2 2c2 c2

c.4m n 12m 7n

d.4x 2(3x 4) 5(2x)

70.Check to determine whether 6 is a solution of 5x 9 x 16. [Section 8.3]

Solve each equation and check the result. [Section 8.4]

x	2 5	72. 4x 40 20
71. 8

73.3(2p 15) 3p 4(11 p)

74.x 2 13

75.OBSERVATION HOURS To pass a teacher education course, a student must have 90 hours of classroom observation time. If a student has already observed for 48 hours, how many 6-hour classroom visits must she make to meet the requirement? (Hint: Form an equation and solve it to answer the question.) [Section 8.5]

76.Identify the base and the exponent of each expression. [Section 8.6]

a.	48	b.	3s4
77. Simplify each expression. [Section 8.6]
a. s4 s5 s		b. (a5)7
c.	(r2t4)(r3t5)	d. (2b3c6)3
e.	(y5)2(y4)3	f.	C( 5.5)3 D12

78. Fill in the blanks. [Section 9.1]

a.	The measure of an		angle is less than 90°.
b.	The measure of a	angle is 90°.
c.	The measure of an			angle is greater than
	90° but less than 180°.
d.	The measure of a straight angle is				.

79.a. Find the supplement of an angle of 105°.

[Section 9.1]

b.Find the complement of an angle of 75°.

[Section 9.1]

80.Refer to the ﬁgure below, where l1 l2. Find the measure of each angle. [Section 9.2]

a.	m( 1)		b.	m( 3)
c.	m( 2)		d.	m( 4)
		l3
	4
	l1
	l1		3
	2		3
	l2		1	130°
	l2

81.Refer to the ﬁgure below, where AB DE and m(AC) m(BC). Find the measure of each angle.

[Section 9.3]

a.	m( 1)			b. m( C)
c.	m( 2)			d. m( 3)
		C
	D	1	E

		2
		2
	A	75°		3
	A			B
				B

82.JAVELIN THROW Refer to the illustration below. Determine x and y. [Section 9.3]

44°

y° x°

83.If the vertex angle of an isosceles triangle measures 34°, what is the measure of each base angle?

[Section 9.3]

84.If the legs of a right triangle measure 10 meters and 24 meters, how long is the hypotenuse? [Section 9.4]

85.Determine whether a triangle with sides of length 16 feet, 63 feet, and 65 feet is a right triangle.

[Section 9.4]

86.SHADOWS If a tree casts a 35-foot shadow at the same time as a man 6 feet tall casts a 5-foot shadow, how tall is the tree? [Section 9.5]

87.Find the sum of the angles of a pentagon. [Section 9.6]

88.Find the perimeter and the area of a square that has sides each 12 meters long. [Section 9.7]

89.Find the area of a triangle with a base that is 14 feet long and a height of 18 feet. [Section 9.7]

90.Find the area of a trapezoid that has bases that are 12 inches and 14 inches long and a height of 7 inches.

[Section 9.7]

91.How many square inches are in 1 square foot?

[Section 9.7]

92.Find the circumference and the area of a circle that has a diameter of 14 centimeters. For each, give the exact answer and an approximation to the nearest hundredth. [Section 9.8]

Chapter 9 Cumulative Review

843

93.Find the area of the shaded region shown below, which is created using two semicircles. Round to the nearest hundredth. [Section 9.8]

19.2 yd

20.2 yd

94.ICE Find the volume of a block of ice that is in the shape of a rectangular solid with dimensions

15 in. 24 in. 18 in. [Section 9.9]

95.Find the volume of a sphere that has a diameter of 18 inches. Give the exact answer and an

approximation to the nearest hundredth. [Section 9.9]

96.Find the volume of a cone that has a circular base with a radius of 4 meters and a height of 9 meters. Give the exact answer and an approximation to the nearest hundredth. [Section 9.9]

97.Find the volume of a cylindrical pipe that is 20 feet long and has a radius of 1 foot. Give the exact answer and an approximation to the nearest hundredth.

[Section 9.9]

98.How many cubic inches are there in 1 cubic foot?

[Section 9.9]

APPENDIX

Addition and

Multiplication Facts

S E C T I O N I.1

Addition Table and One Hundred Addition and Subtraction Facts

Table of Basic Addition Facts

	0	1	2	3	4	5	6	7	8	9
0	0	1	2	3	4	5	6	7	8	9
1	1	2	3	4	5	6	7	8	9	10
2	2	3	4	5	6	7	8	9	10	11
3	3	4	5	6	7	8	9	10	11	12
4	4	5	6	7	8	9	10	11	12	13
5	5	6	7	8	9	10	11	12	13	14
6	6	7	8	9	10	11	12	13	14	15
7	7	8	9	10	11	12	13	14	15	16
8	8	9	10	11	12	13	14	15	16	17
9	9	10	11	12	13	14	15	16	17	18

A-1

A-2 Appendix I Addition and Multiplication Facts

Fifty Addition Facts

1.	3	2.	1	3.	2	4.	5
	2		1		5		4
5.	7	6.	1	7.	6	8.	9
	7		8		6		4
9.	3	10.	0	11.	6	12.	5
	8		4		3		1
13.	2	14.	4	15.	1	16.	7
	8		7		6		2
17.	8	18.	4	19.	7	20.	1
	9		3		0		3
21.	4	22.	8	23.	9	24.	5
	6		6		9		9
25.	0	26.	2	27.	7	28.	8
	8		2		6		8
29.	1	30.	4	31.	4	32.	5
	2		2		4		6
33.	3	34.	9	35.	2	36.	6
	3		7		6		9
37.	0	38.	8	39.	7	40.	5
	6		5		3		5
41.	1	42.	4	43.	3	44.	8
	0		1		5		4
45.	9	46.	3	47.	7	48.	1
	2		9		8		9
49.	5	50.	7
	7		1

Fifty Subtraction Facts

1.	8	2.	8	3.	4	4.	4
	5		7		2		3
5.	7	6.	14	7.	12	8.	11
	3		7		8		5
9.	12	10.	10	11.	18	12.	8
	3		8		9		6
13.	10	14.	6	15.	15	16.	9
	4		3		9		5
17.	2	18.	10	19.	15	20.	10
	0		5		7		1
21.	17	22.	7	23.	13	24.	9
	8		1		6		0
25.	16	26.	12	27.	7	28.	11
	8		5		5		7
29.	14	30.	16	31.	5	32.	6
	5		7		0		4
33.	12	34.	14	35.	5	36.	11
	6		6		3		3
37.	13	38.	7	39.	9	40.	2
	8		0		1		1
41.	3	42.	9	43.	13	44.	11
	2		3		9		2
45.	10	46.	6	47.	4	48.	8
	3		1		0		4
49.	9	50.	5
	2		4

Appendix I Addition and Multiplication Facts

A-3

S E C T I O N I.2

Multiplication Table and One Hundred Multiplication and Division Facts

Table of Basic Multiplication Facts

	0	1	2	3	4	5	6	7	8	9
0	0	0	0	0	0	0	0	0	0	0
1	0	1	2	3	4	5	6	7	8	9
2	0	2	4	6	8	10	12	14	16	18
3	0	3	6	9	12	15	18	21	24	27
4	0	4	8	12	16	20	24	28	32	36
5	0	5	10	15	20	25	30	35	40	45
6	0	6	12	18	24	30	36	42	48	54
7	0	7	14	21	28	35	42	49	56	63
8	0	8	16	24	32	40	48	56	64	72
9	0	9	18	27	36	45	54	63	72	81

A-4 Appendix I Addition and Multiplication Facts

Fifty Multiplication Facts

1.	4	2.	1	3.	6	4.	9
	4		4		3		7
5.	5	6.	0	7.	5	8.	1
	7		8		2		2
9.	7	10.	4	11.	3	12.	9
	8		0		3		3
13.	5	14.	7	15.	3	16.	8
	6		2		5		8
17.	1	18.	3	19.	0	20.	6
	8		2		7		4
21.	8	22.	9	23.	6	24.	1
	6		9		0		3
25.	4	26.	8	27.	9	28.	7
	8		2		1		7
29.	9	30.	1	31.	9	32.	4
	6		5		0		5
33.	8	34.	7	35.	6	36.	7
	3		6		2		1
37.	5	38.	4	39.	7	40.	1
	8		3		4		1
41.	9	42.	2	43.	7	44.	2
	5		2		3		4
45.	6	46.	9	47.	5	48.	6
	6		2		5		1
49.	8	50.	9
	9		4

Fifty Division Facts


1.	4	20		2.	8	56		3.	3	6		4.	1	8
	9				7				5				3
5.	9	45		6.	7	42		7.	5	25		8.	3	24
	5				7				9				3
9.	5	5		10.	7		21	11.	9		81	12.	3		0
	8				6				9				2
13.	8		32	14.	6		18	15.	9		0	16.	2		10
	4				3				1				6
17.	4		8	18.	3		27	19.	1		1	20.	6		30
	1				4				7				5
21.	1		7	22.	4		16	23.	7		63	24.	5		0
	7				3				5				8
25.	7		35	26.	3		3	27.	5		15	28.	8		48
	7				2				3				6
29.	7		0	30.	2		16	31.	3		9	32.	6		12
	9				8				4				8
33.	9		72	34.	8		0	35.	4		28	36.	8		64
	6				6				7				7
37.	6		24	38.	6		54	39.	7		49	40.	7		14
	6				1				3				4
41.	6		36	42.	1		9	43.	3		12	44.	4		36
	2				8				2				1
45.	2		4	46.	8		40	47.	2		2	48.	1		4
	9				6
49.	9		18	50.	6		6

EXAMPLE 1

APPENDIX

Polynomials

Objectives

S E C T I O N II.1

1Know the vocabulary for polynomials.

Introduction to Polynomials

2 Evaluate polynomials.	1	Know the vocabulary for polynomials.

Recall that an algebraic term, or simply a term, is a number or a product of a number and one or more variables, which may be raised to powers. Some examples of terms are

17,

5x,

6t 2,

and

8z3

The coefﬁcients of these terms are 17, 5, 6, and 8, in that order.

Self Check 1

Classify each polynomial as a monomial, a binomial, or a trinomial:

a.8x2 7

b.5x

c.x2 2x 1

Now Try Problems 5, 7, and 11

Polynomials

A polynomial is a single term or a sum of terms in which all variables have whole-number exponents and no variable appears in the denominator.

Some examples of polynomials are

141, 8y2, 2x 1, 4y2 2y 3, and 7a3 2a2 a 1

The polynomial 8y2 has one term.The polynomial 2x 1 has two terms, 2x and 1. Since 4y2 2y 3 can be written as 4y2 ( 2y) 3, it is the sum of three terms, 4y2, 2y, and 3.

We classify some polynomials by the number of terms they contain.A polynomial with one term is called a monomial. A polynomial with two terms is called a binomial. A polynomial with three terms is called a trinomial. Some examples of these polynomials are shown in the table below.

Monomials	Binomials	Trinomials

5x2	2x 1	5t 2 4t 3
6x	18a2 4a	27x3 6x 2
29	27z4 7z2	32r2 7r 12

Classify each polynomial as a monomial, a binomial, or a trinomial: a. 3x 4 b. 3x2 4x 12 c. 25x3

Strategy We will count the number of terms in the polynomial.

WHY The number of terms determines the type of polynomial.

Solution

a.Since 3x 4 has two terms, it is a binomial.

b.Since 3x2 4x 12 has three terms, it is a trinomial.

c. Since 25x3 has one term, it is a monomial.

A-5

A-6	Appendix II Polynomials

Self Check 2

Find the degree of each polynomial:

a.3p3

b.17r4 2r8 r

c.2g5 7g6 12g7

Now Try Problems 13, 15, and 17

The monomial 7x3 is called a monomial of third degree or a monomial of degree 3, because the variable occurs three times as a factor.

• 5x2 is a monomial of degree 2.			Because the variable occurs two times
			as a factor: x2 x x.
• 8a4 is a monomial of degree 4.			Because the variable occurs four times
			as a factor: a4 a a a a.
•	1	m5 is a monomial of degree 5.	Because the variable occurs ﬁve times

2			as a factor: m5 m m m m m.

We deﬁne the degree of a polynomial by considering the degrees of each of its terms.

Degree of a Polynomial

The degree of a polynomial is the same as the degree of its term with largest degree.

For example,

•x2 5x is a binomial of degree 2, because the degree of its term with largest degree (x2) is 2.

•4y3 2y 7 is a trinomial of degree 3, because the degree of its term with largest degree (4y3) is 3.

•12 z 3z4 2z2 is a trinomial of degree 4, because the degree of its term with largest degree (3z4) is 4.

EXAMPLE 2 Find the degree of each polynomial: a. 2x 4 b. 5t 3 t 4 7 c. 3 9z 6z2 z3

Strategy We will determine the degree of each term of the polynomial.

WHY The term with the highest degree gives the degree of the polynomial.

Solution

a.Since 2x can be written as 2x1, the degree of the term with largest degree is 1. Thus, the degree of the polynomial 2x 4 is 1.

b.In 5t 3 t 4 7, the degree of the term with largest degree (t 4) is 4. Thus, the degree of the polynomial is 4.

c.In 3 9z 6z2 z3, the degree of the term with largest degree ( z3) is 3. Thus,

the degree of the polynomial is 3.

2 Evaluate polynomials.

When a number is substituted for the variable in a polynomial, the polynomial takes on a numerical value. Finding this value is called evaluating the polynomial.

EXAMPLE 3 Evaluate each polynomial for x 3: a. 3x 2 b. 2x2 x 3

Strategy We will substitute the given value for each x in the polynomial and follow the order of operations rule.

EXAMPLE 4

WHY To evaluate a polynomial means to ﬁnd its numerical value, once we know the value of its variable.

Solution
a. 3x 2 313	2 2	Substitute 3 for x.
9 2		Multiply: 3(3) 9.
7		Subtract.

b.2x2 x 3 2132 2 3 3

219 2 3 3

18 3 3

15 3

Substitute 3 for x.

Evaluate the exponential expression. Multiply: 2(9) 18.

Add: 18 3 15.

Subtract: 15 3 15 ( 3) 18.

Height of an Object The polynomial 16t 2 28t 8 gives the height (in feet) of an object t seconds after it has been thrown into the air. Find the height of the object after 1 second.

Strategy We will substitute 1 for t and evaluate the polynomial.

WHY The variable t represents the time since the object was thrown into the air.

Solution

To ﬁnd the height at 1 second, we evaluate the polynomial for t 1.

16t2 28t 8 16112 2 28112 8			Substitute 1 for t.
		1611 2 2811 2 8	Evaluate the exponential expression.
		16 28 8	Multiply: 16(1) 16 and 28(1) 28.
		12 8	Add: 16 28 12.
		20	Add.
At 1 second, the height of the object is 20 feet.
At 1 second, the height of the object is 20 feet.

ANSWERS TO SELF CHECKS
ANSWERS TO SELF CHECKS
1.	a. binomial	b. monomial c. trinomial 2.	a. 3 b. 8 c. 7
3.	a. 6 b. 8	4. 0 ft

S E C T I O N II.1		STUDY SET
	VOCABULARY		CONCEPTS

Appendix II Polynomials

A-7

Self Check 3

Evaluate each polynomial for x 1:

a.2x2 4

b.3x2 4x 1

Now Try Problems 23 and 31

Self Check 4

Refer to Example 4. Find the height of the object after

2 seconds.

Now Try Problems 35 and 37

Fill in the blanks.
1.	A polynomial with one term is called a		.
2.	A polynomial with three terms is called a		.
3.	A polynomial with two terms is called a		.
4.	The degree of a polynomial is the same as the degree
	of its term with	degree.

Classify each polynomial as a monomial, a binomial, or a trinomial.

5.	3x2 4	6.	5t2 t 1
7.	17e4	8.	x2 x 7
9.	25u2	10.	x2 9
11. q5 q2 1		12.	4d3 3d2

A-8					Appendix II Polynomials
	Find the degree of each polynomial.
13.			5x3				14.					3t 5 3t 2
			2x	2	3x 2							1		4				2
15.							16.						p		p
15.							16.					2	p		p
17.			2m				18.					7q 5
19.			25w6 5w7				20.					p6 p8
		NOTATION
		NOTATION
	Complete each solution.
21.			Evaluate 3a2 2a 7 for a 2.
					3a2 2a 7 31					22 21						2 7
					3a2 2a 7 31					22 21						2 7
					31				2					7
					31				2					7
					12 4 7
											7
											7
					9
22.			Evaluate q2 3q 2 for q 1.
			q2 3q 2 1					22 31									2 2
			q2 3q 2 1					22 31									2 2
					1	2 31 1 2 2
					1	2 31 1 2 2

1 2

PRACTICE

Evaluate each polynomial for the given value.

23.3x 4 for x 3

24.12 x 3 for x 6

25.2x2 4 for x 1

26.12 x2 1 for x 2

27.0.5t 3 1 for t 4

28.0.75a2 2.5a 2 for a 0

29.23 b2 b 1 for b 3

30.3n2 n 2 for n 2

31.2s2 2s 1 for s 1

32.4r2 3r 1 for r 2

APPLICATIONS

The height h (in feet) of a ball shot straight up with an initial velocity of 64 feet per second is given by the equation h 16t2 64t. Find the height of the ball after the given number of seconds.

33.	0 second	34.	1 second
35.	2 seconds	36.	4 seconds

The number of feet that a car travels before stopping depends on the driver’s reaction time and the braking distance. For one driver, the stopping distance d is given by the equation

d 0.04v2 0.9v, where v is the velocity of the car. Find the stopping distance for each of the following speeds.

37.	30 mph	38.	50 mph
39.	60 mph	40.	70 mph

Decision

to stop

WRITING

41.Explain how to ﬁnd the degree of the polynomial 2x3 5x5 7x.

42.Explain how to evaluate the polynomial 2x2 3 for x 5.

REVIEW

Perform the operations.


43.	2			4	44.	36	23
43.	3		3		44.	7	7
45.	5	#	18		46.	23	46
45.	12	#	5		46.	25	5
	12		5			25	5
Solve each equation.
47.	x 4 12				48.	4z 108
49.	2(x 3) 6				50.	3(a 5) 4(a 9)

Objectives		S E C T I O N II.2
	Add polynomials.	Adding and Subtracting Polynomials
1
	Subtract polynomials.	Polynomials can be added, subtracted, and multiplied just like numbers in arithmetic.

2

In this section, we show how to ﬁnd sums and differences of polynomials.

EXAMPLE 2

Appendix II Polynomials

A-9

1 Add polynomials.

Recall that like terms have exactly the same variables and the same exponents. For example, the monomials

3z2	and	2z2	are like terms	Both have the same variable (z) with the same
				exponent (2).
However, the monomials
7b2	and	8a2	are not like terms	They have different variables.
32p2	and	25p3 are not like terms The exponents of p are different.

Also recall that we use the distributive property in reverse to simplify a sum or difference of like terms. We combine like terms by adding their coefﬁcients and keeping the same variables and exponents. For example,

2y 5y 12 5 2y	and 3x2 7x2 1 3 7 2x2
7y	4x2

These examples suggest the following rule.

Adding Polynomials

To add polynomials, combine their like terms.

EXAMPLE 1 Add: 5x3 7x3

Strategy We will use the distributive property in reverse and add the coefﬁcients of the terms.

WHY 5x3 and 7x3 are like terms and therefore can be added.

Solution

5x3 7x3 12x3 Think: (5 7)x3 12x3.

Add: 32 t2 52 t2 72 t2

Strategy We will use the distributive property in reverse and add the coefﬁcients of the terms.

WHY 32t2, 52t2, and 72t2 are like terms and therefore can be added.

Solution

Since the three monomials are like terms, we add the coefﬁcients and keep the variables and exponents.

3	t	2	5	t	2	7	t	2	a		3			5	7	bt	2
2	t		2	t		2	t		a		2			2	2	bt
										15			2
										15		t	2					To add the fractions, add the numerators
																		and keep the denominator: 3 5 7 15.
										2
										2

To add two polynomials, we write a sign between them and combine like terms.

EXAMPLE 3 Add: 2x 3 and 7x 1

Strategy We will reorder and regroup to get the like terms together. Then we will combine like terms.

Self Check 1

Add: 7y3 12y3

Now Try Problems 15 and 19

Self Check 2

Add:

19 a3 29 a3 59 a3

Now Try Problem 21

Self Check 3

Add:

5y 2 and 3y 7

Now Try Problem 27

WHY To add polynomials means to combine their like terms.

A-10	Appendix II Polynomials

Self Check 4

Add:

(2b2 4b) (b2 3b 1)

Now Try Problem 33

Self Check 5

Add:

(s2 1.2s 5) (3s2 2.5s 4)

Now Try Problem 37

Solution

12x 3 2 17x 1 2	Write a sign between the binomials.
12x 7x 2 13 1 2	Use the associative and commutative properties to
	group like terms together.
9x 2	Combine like terms.

The binomials in Example 3 can be added by writing the polynomials so that like terms are in columns.

2x 3

7x 1

9x 2 Add the like terms, one column at a time.

EXAMPLE 4 Add: (5x2 2x 4) (3x2 5)

Strategy We will combine the like terms of the trinomial and binomial.

WHY To add polynomials, we combine like terms.

Solution

15x2 2x 4 2 13x2 5 2

15x2 3x2 2 1 2x 2 14 5 2	Use the associative and commutative
	properties to group like terms together.
8x2 2x 1	Combine like terms.
8x2 2x 1	Combine like terms.

The polynomials in Example 4 can be added by writing the polynomials so that like terms are in columns.

	5x2	2x 4
3x2		5
	8x2	2x 1	Add the like terms, one column at a time.

	EXAMPLE 5 Add:	(3.7x2 4x 2) (7.4x2 5x 3)
	EXAMPLE 5 Add:	(3.7x2 4x 2) (7.4x2 5x 3)
Strategy We will combine the like terms of the two trinomials.
WHY To add polynomials, we combine like terms.
Solution
	13.7x2 4x 2 2 17.4x2 5x 3 2
	13.7x2 7.4x2 2	14x 5x 2 1 2 3 2 Use the associative and
		commutative properties to
		group like terms together.
	11.1x2 x 1	Combine like terms.

The trinomials in Example 5 can be added by writing them so that like terms are in columns.

	3.7x2	4x 2
7.4x2		5x 3
	11.1x2	x 1	Add the like terms, one column at a time.

2 Subtract polynomials.

To subtract one monomial from another, we add the opposite of the monomial that is to be subtracted. In symbols, x y x ( y).

EXAMPLE 6 Subtract: 8x2 3x2

Strategy We will add the opposite of 3x2 to 8x2.

WHY To subtract monomials, we add the oppostie of the monomial that is to be subtracted.

Solution

8x2 3x2 8x2 1 3x2 2	Add the opposite of 3x2.
5x2	Add the coefﬁcients and keep the same variable and
	exponent. Think: [8 ( 3)]x 2 5x2
	exponent. Think: [8 ( 3)]x 2 5x2

Recall from Chapter 1 that we can use the distributive property to ﬁnd the opposite of several terms enclosed within parentheses. For example, we consider(2a2 a 9).

(2a2 a 9) 1(2a2 a 9)	Replace the symbol in front
	of the parentheses with 1.
2a2 a 9	Use the distributive property
	to remove parentheses.

This example illustrates the following method of subtracting polynomials.

Subtracting Polynomials

To subtract two polynomials, change the signs of the terms of the polynomial being subtracted, drop the parentheses, and combine like terms.

EXAMPLE 7 Subtract: (3x 4.2) (5x 7.2)

Strategy We will change the signs of the terms of 5x 7.2, drop the parentheses, and combine like terms.

WHY This is the method for subtracting two polynomials.

Solution

(3x 4.2) (5x 7.2)

3x 4.2 5x 7.2	Change the signs of each term of 5x 7.2
	and drop the parentheses.
2x 11.4	Combine like terms: Think: (3 5)x 2x
	and ( 4.2 7.2) 11.4.
	and ( 4.2 7.2) 11.4.

The binomials in Example 7 can be subtracted by writing them so that like terms are in columns.

	3x 4.2	3x 4.2
1	5x 7.2 2	¡ 5x	7.2	Change signs and add, column by column.
		2x	11.4

Appendix II Polynomials

A-11

Self Check 6

Subtract: 6y3 9y3

Now Try Problem 47

Self Check 7

Subtract:

(3.3a 5) (7.8a 2)

Now Try Problem 51

A-12 Appendix II Polynomials

Self Check 8

Subtract:

(5y2 4y 2) (3y2 2y 1)

Now Try Problem 59

EXAMPLE 8 Subtract: (3x2 4x 6) (2x2 6x 12)

Strategy We will change the signs of the terms of 2x2 6x 12, drop the parentheses, and combine like terms.

WHY This is the method for subtracting two polynomials.

Solution

(3x2 4x 6) (2x2 6x 12)

3x2 4x 6 2x2 6x 12	Change the signs of each term of 2x2
	6x 12 and drop the parentheses.
x2 2x 18	Combine like terms: Think: (3 2)x2 x2,
	( 4 6)x 2x, and ( 6 12) 18.

The trinomials in Example 8 can be subtracted by writing them so that like terms are in columns.

		3x2 4x 6		3x2 4x 6		Change signs and add,
	1 2x2 6x 12 2 ¡			2x2	6x 12	Change signs and add,
	1 2x2 6x 12 2 ¡			2x2	6x 12	column by column.
				x2	2x 18	column by column.
				x2	2x 18

ANSWERS TO SELF CHECKS
ANSWERS TO SELF CHECKS
1.	19y3 2. 98 a3		3. 2y 5 4.	3b2 b 1 5. 4s2 1.3s 1 6. 3y3
7.	4.5a 7 8.		2y2 6y 3

S E C T I O N II.2

STUDY SET

VOCABULARY

Fill in the blanks.

If two algebraic terms have exactly the same variables

and exponents, they are called

terms.

3x3 and 3x2 are

terms.

CONCEPTS

Fill in the blanks.

To add two monomials, we add the

and

keep the same

and exponents.

To subtract one monomial from another, we add the

of the monomial that is to be subtracted.

Determine whether the monomials are like terms. If they are, combine them.

5.	3y, 4y	6.	3x2, 5x2
7.	3x, 3y	8.	3x2, 6x
9.	3x3, 4x3, 6x3	10.	2y4, 6y4, 10y4
11.	5x2, 13x2, 7x2	12.	23, 12x, 25x

NOTATION

Complete each solution.

13.13x2 2x 5 2 1 2x2 7x 2

1 3x2 2 12x 2 1 5 2

1 5x 2 5

5x2 5x 5

14.1 3x2 2x 5 2 1 2x2 7x 2

1 3x2 2x 5 2 3 1 7x 2 4

1 3x2 2x 5 2 1

1 2 1 2x 7x 2 1 5 2

x2 9x 5

PRACTICE

Add the polynomials.
15.	4y 5y			16.	2x 3x
17.	8t2	4t2		18.	15x2 10x2
19.	3s2	4s2	7s2	20.	2a3 7a3 3a3


21.	1	a	3		a		5		a			22.		1	b	3		b		1	b
21.	8	a	8		a		8		a			22.		4	b	4		b		4	b
	2	2	1			2		2			2			4	3	1			3			3		3
23.		c				c				c			24.		d				d				d
	3			3				3						9			9					9
	3			3				3						9			9					9

25.Add: 3x 7 and 4x 3

26.Add: 2y 3 and 4y 7

27.Add: 2x2 3 and 5x2 10

28.Add: 4a2 1 and 5a2 1

29.(5x3 42x) (7x3 107x)

30.( 43a3 25a) (58a3 10a)

31.(3x2 2x 4) (5x2 17)

32.(5a2 2a) ( 2a2 3a 4)

33.(7y2 5y) (y2 y 2)

34.(4p2 4p 5) (6p 2)

35.(3x2 3x 2) (3x2 4x 3)

36.(4c2 3c 2) (3c2 4c 2)

37.(2.5a2 3a 9) (3.6a2 7a 10)

38.(1.9b2 4b 10) (3.7b2 3b 11)

39.(3n2 5.8n 7) ( n2 5.8n 2)

40.( 3t2 t 3.4) (3t 2 2t 1.8)

41.		3x2 4x 5		42.			2x2	3x 5
	2x2 3x 6				4x2 x 7
43.		3x2	7	41.		4x2 4x 9
	4x2 5x 6							9x 3
45.		3x2	4x 25.4	46.		6x3		4.2x2 7
	5x2		3x 12.5		7x3			9.7x2 21

Subtract the polynomials.
47.	32u3 16u3			48.	25y2		7y2
49.	18x5 11x5			50.	17x6		22x6

51.(30x2 4) (11x2 1)

52.(5x3 8) (2x3 5)

53.(3x2 2x 1) ( 4x2 4)

54.(7a2 5a) (5a2 2a 3)

55.(4.5a 3.7) (2.9a 4.3)

56.(5.1b 7.6) (3.3b 5.9)

57.(2b2 3b 5) (2b2 4b 9)

58.(3a2 2a 4) (a2 3a 7)

59.(5p2 p 71) (4p2 p 71)

60.(m2 m 5) (m2 5.5m 75)

61.(3.7y2 5) (2y2 3.1y 4)

62.(t 2 4.5t 5) (2t2 3.1t 1)

						Appendix II		Polynomials		A-13
63.			3x2 4x 5			64.		3y2 4y 7
	1		2x2 2x 3	2			1	6y2 6y 13 2
								25x3 45x2 31x
65.		2x2 4x 12				66.		25x3 45x2 31x
	1		10x2 9x 24		2		1	12x3 27x2 17x		2
		4x3 3x 10
67.		4x3 3x 10				68.		3x3 4x2 12
	1		5x3 4x 4 2				1	4x3 6x2 3	2

APPLICATIONS

In Exercises 69–72, recall that the perimeter of a ﬁgure is equal to the sum of the lengths of its sides.

69.THE RED CROSS In 1891, Clara Barton founded the Red Cross. Its symbol is a white ﬂag bearing a red cross. If each side of the cross has length x, write an expression that represents the perimeter of the cross.

70.BILLIARDS Billiard tables vary in size, but all tables are twice as long as they are wide.

a.If the billiard table is x feet wide, write an expression that represents its length.

b.Write an expression that represents the perimeter of the table.

xft

71.PING-PONG Write an expression that represents the perimeter of the Ping-Pong table.

A-14	Appendix II Polynomials
72.	SEWING Write an expression that represents the
	length of the yellow trim needed to outline a pennant
	with the given side lengths.

		(2x
		– 15)		cm
				cm
		x cm DOLPHINS
		x	–15)	cm
		x	–15)
		(2

WRITING

73.What are like terms?

74.Explain how to add two polynomials.

75.Explain how to subtract two polynomials.

76.When two binomials are added, is the result always a binomial? Explain.

REVIEW

77.BASKETBALL SHOES Use the following information to ﬁnd how much lighter the Kevin Garnett shoe is than the Michael Jordan shoe.

Nike Air Garnett III	Air Jordan XV
Synthetic fade mesh	Full grain leather upper
and leather.	with woven pattern.
1	1
Sizes 6 – –18	Sizes 6 – –18
2	2
Weight: 13.8 oz	Weight: 14.6 oz

78.AEROBICS The number of calories burned when doing step aerobics depends on the step height. How many more calories are burned during a 10-minute workout using an 8-inch step instead

of a 4-inch step?

Step height (in.)	Calories burned per minute

4	4.5
6	5.5
8	6.4
10	7.2

Source: Reebok Instructor News (Vol. 4, No. 3, 1991)

79.THE PANAMA CANAL A ship entering the Panama Canal from the Atlantic Ocean is lifted up 85 feet to Lake Gatun by the Gatun Lock system. See the illustration. Then the ship is lowered 31 feet by the Pedro Miguel Lock. By how much must the ship be lowered by the Miraﬂores Lock system for it to reach the Paciﬁc Ocean water level?

80.CANAL LOCKS What is the combined length of the system of locks in the Panama Canal? Express your answer as a mixed number and as a decimal, rounded to the nearest tenth.

Gatun Locks		Pedro Miguel Lock
Gatun Locks	Gatun	5/6 mile long
1.5 miles long		5/6 mile long
		Miraflores Locks
	Lake
	Lake
Atlantic		1 mile long	Pacific
Atlantic			Pacific
Ocean			Ocean

Same mean sea level

Objectives

S E C T I O N II.3

1 Multiply monomials.

Multiplying Polynomials

2Multiply a polynomial by a monomial.

3Multiply binomials.

4Multiply polynomials.

We now discuss how to multiply polynomials. We will begin with the simplest case— ﬁnding the product of two monomials.

1 Multiply monomials.

To multiply 4x2 by 2x3, we use the commutative and associative properties of multiplication to reorder and regroup the factors.

(4x2 )(2x3 ) (4 2)(x2 x3 )	Group the coefﬁcients together
	and the variables together.
8x5	Simplify: x2 x3 x2 3 x5.

This example suggests the following rule.

Appendix II Polynomials

A-15

Multiplying Two Monomials

To multiply two monomials, multiply the numerical factors (the coefﬁcients) and then multiply the variable factors.

EXAMPLE 1 Multiply: a. 3y 6y b. 3x5(2x5)

Strategy We will multiply the numerical factors and then multiply the variable factors.

WHY The commutative and associative properties of multiplication enable us to reorder and regroup factors.

Solution		#6 21y #y 2
a.	3y #6y 13	#6 21y #y 2	Group the numerical factors and group the variables.
	18y2		Multiply: 3 6 18 and y y y2.
b.	1 3x5 212x5 2	1 3 #2 21x5 #x5 2 Group the numerical factors
			and group the variables.
		6x10	Multiply: 3 2 6 and x5 x5 x5 5 x10.
		6x10	Multiply: 3 2 6 and x5 x5 x5 5 x10.

2 Multiply a polynomial by a monomial.

To ﬁnd the product of a polynomial and a monomial, we use the distributive property. To multiply x 4 by 3x, for example, we proceed as follows:

3x 1x 4 2 3x 1x 2 3x 14 2	Use the distributive property.
3x2 12x	Multiply the monomials: 3x(x) 3x2 and 3x(4) 12x.

The results of this example suggest the following rule.

Self Check 1

Multiply: 7a3 2a5

Now Try Problem 15

Multiplying Polynomials by Monomials

To multiply a polynomial by a monomial, multiply each term of the polynomial by the monomial.

EXAMPLE 2 Multiply: a. 2a2(3a2 4a) b. 8x(3x2 2x 3)

Strategy We will multiply each term of the polynomial by the monomial.

WHY We use the distributive property to multiply a monomial and a polynomial.

Solution

a.2a2 13a2 4a 2

2a2 13a2 2 2a2 14a 2 Use the distributive property.

6a4 8a3 Multiply: 2a2(3a2) 6a4 and 2a2(4a) 8a3.

b. 8x(3x2 2x 3)

8x(3x2 ) 8x(2x ) 8x(3)	Use the distributive property.
24x3 16x2 24x	Multiply: 8x(3x2) 24x3, 8x(2x) 16x2,
	and 8x(3) 24x.
	and 8x(3) 24x.

Self Check 2

Multiply:

a.3y(5y3 4y)

b.5x(3x2 2x 3)

Now Try Problem 29

A-16	Appendix II Polynomials

3 Multiply binomials.

The distributive property can also be used to multiply binomials. For example, to multiply 2a 4 and 3a 5, we think of 2a 4 as a single quantity and distribute it over each term of 3a 5.

(2a 4)(3a 5) (2a 4)3a (2a 4)5
(2a 4)3a (2a 4)5
(2a)3a (4)3a (2a)5 (4)5		Distribute the multiplication
		by 3a and by 5.
6a2	12a 10a 20	Multiply the monomials.
6a2	22a 20	Combine like terms.

In the third line of by each term of 2a

the solution, notice that each term of 3a 5 has been multiplied4. This example suggests the following rule.

Multiplying Binomials

To multiply two binomials, multiply each term of one binomial by each term of the other binomial, and then combine like terms.

We can use a shortcut method, called the FOIL method, to multiply binomials. FOIL is an acronym for First terms, Outer terms, Inner terms, Last terms. To use the FOIL method to multiply 2a 4 by 3a 5, we

1.multiply the First terms 2a and 3a to obtain 6a2,

2.multiply the Outer terms 2a and 5 to obtain 10a,

3.multiply the Inner terms 4 and 3a to obtain 12a, and

4.multiply the Last terms 4 and 5 to obtain 20.

Then we simplify the resulting polynomial, if possible.

Outer
First		F	O	I	L
		F	O	I	L
(2a 4)(3a 5) 2a(3a) 2a(5) 4(3a) 4(5)
Inner
Last
	6a2	10a 12a 20			Multiply the monomials.
	6a2	22a 20			Combine like terms.

The Language of Algebra An acronym is an abbreviation of several words in such a way that the abbreviation itself forms a word. The acronym FOIL helps us remember the order to follow when multiplying two binomials: First, Outer, Inner, Last.

EXAMPLE 3 Multiply: a. (x 5)(x 7) b. (3x 4)(2x 3)

Strategy We will use the FOIL method.

WHY In each case we are to ﬁnd the product of two binomials, and the FOIL method is a shortcut for multiplying two binomials.

Solution

a.	O
	F
	F	O	I	L

(x 5)(x 7) x(x) x(7) 5(x) 5(7)

I L

b.O

(3x 4)(2x

I L


x2 7x 5x 35					Multiply the monomials.
x2 12x 35					Combine like terms.
	F		O	I	L
3)	3x(2x) 3x( 3) 4(2x) 4( 3)
	6x2	9x 8x 12			Multiply the monomials.
	6x2	x 12			Combine like terms.

EXAMPLE 4 Find: (5x 4)2

Strategy We will write the base, 5x 4, as a factor twice, and perform the multiplication.

WHY In the expression (5x 4)2, the binomial 5x 4 is the base and 2 is the exponent.

Solution

	F
(5x 4)2 (5x 4)(5x 4)			Write the base as a factor twice.
	I L
F	O	I	L
5x(5x) 5x( 4) ( 4)(5x) ( 4)( 4)
25x2	20x 20x 16		Multiply the monomials.
25x2	40x 16		Combine like terms.
25x2	40x 16		Combine like terms.

Caution! A common error when squaring a binomial is to square only its

ﬁrst and second terms. For example, it is incorrect to write

15x 4 22 15x 22 14 22

25x2 16

The correct answer is 25x2 40x 16.

4 Multiply polynomials.

To develop a general rule for multiplying any two polynomials, we will ﬁnd the product of 2x 3 and 3x2 3x 5. In the solution, the distributive property is used four times.

(2x 3)(3x2 3x 5)
(2x 3)3x2 (2x 3)3x (2x 3)5		Distribute.
(2x 3)3x2 (2x 3)3x (2x 3)5
(2x)3x2 (3)3x2 (2x)3x (3)3x (2x)5 (3)5		Distribute.
6x3	9x2 6x2 9x 10x 15	Multiply the monomials.
6x3	15x2 19x 15	Combine like terms.

Appendix II Polynomials

A-17

Self Check 3

Multiply:

a.(y 3)(y 1)

b.(2a 1)(3a 2)

Now Try Problems 35 and 39

Self Check 4

Find: (5x 4)2

Now Try Problem 41

A-18	Appendix II Polynomials

In the third line of the solution, note that each term of 3x2 3x 5 has been multiplied by each term of 2x 3. This example suggests the following rule.

Self Check 5

Multiply:

(3a2 1)(2a4 a2 a)

Now Try Problem 49

Self Check 6

Multiply using vertical form:

a.(3x 2)(2x2 4x 5)

b.( 2x2 3)(2x2 4x 1)

Now Try Problem 63

Multiplying Polynomials

To multiply two polynomials, multiply each term of one polynomial by each term of the other polynomial, and then combine like terms.

EXAMPLE 5 Multiply: (7y 3)(6y2 8y 1)

Strategy We will multiply each term of the trinomial, 6y2 8y 1, by each term of the binomial, 7y 3.

WHY To multiply two polynomials, we must multiply each term of one polynomial by each term of the other polynomial.

Solution

(7y 3)(6y2 8y 1)

7y(6y2) 7y( 8y) 7y(1) 3(6y2) 3( 8y) 3(1)

42y3	56y2	7y 18y2 24y 3	Multiply the monomials.
42y3	38y2	17y 3	Combine like terms.

Caution! The FOIL method cannot be applied here—only to products of two binomials.

It is often convenient to multiply polynomials using a vertical form similar to that used to multiply whole numbers.

Success Tip Multiplying two polynomials in vertical form is much like multiplying two whole numbers in arithmetic.

347

1 735

6 940

8,675

EXAMPLE 6 Multiply using vertical form:

a. (3a2 4a 7)(2a 5) b. (6y3 5y 4)( 4y2 3)

Strategy First, we will write one polynomial underneath the other and draw a horizontal line beneath them. Then, we will multiply each term of the upper polynomial by each term of the lower polynomial.

WHY Vertical form means to use an approach similar to that used in arithmetic to multiply two whole numbers.

Appendix II Polynomials

A-19

Solution

a. Multiply: 3a2 4a 7

		2a 5
	15a2	20a 35
6a3 8a2		14a

6a3 7a2 6a 35

Multiply 3a2 4a 7 by 5. Multiply 3a2 4a 7 by 2a.

In each column, combine like terms.

b.With this method, it is often necessary to leave a space for a missing term to vertically align like terms.

Multiply:		6y3 5y 4
		4y2 3
	18y3	15y 12

24y5 20y3 16y2

24y5 2y3 16y2 15y 12

Multiply 6y3 5y 4 by 3. Multiply 6y3 5y 4 by 4y2.

Leave a space for any missing powers of y. In each column, combine like terms.

ANSWERS TO SELF CHECKS
1.	14a8 2. a. 15y4 12y2 b. 15x3 10x2 15x	3.	a. y2 4y 3 b. 6a2 a 2
4.	25x2 40x 16 5. 6a6 5a4 3a3 a2 a 6.	a.	6x3 8x2 7x 10

b. 4x4 8x3 8x2 12x 3

S E C T I O N

II.3

STUDY SET

VOCABULARY

Fill in the blanks.

(2x3)(3x4) is the product of two

(2a 4)(3a 5) is the product of two

In the acronym FOIL, F stands for

terms, O for

terms, I for

terms, and L for

terms.

(2a 4)(3a2 5a 1) is the product of a

and a

CONCEPTS

Fill in the blanks.

To multiply two polynomials, multiply

term of

one polynomial by

term of the other

polynomial, and then combine like terms.

6.Label each arrow using one of the letters F, O, I, or L. Then ﬁll in the blanks.

First Outer Inner Last

(2x 5)(3x 4)

7.Simplify each polynomial by combining like terms.

a.6x2 8x 9x 12

b.5x4 3ax2 5ax2 3a2

8.a. Add: (x 4) (x 8)

b.Subtract: (x 4) (x 8)

c.Multiply: (x 4)(x 8)

NOTATION

Complete each solution.

9.(9n3)(8n2) (9 )( n2)

10.7x(3x2 2x 5) (3x2) (2x) (5)

14x2 35x

11.(2x 5)(3x 2) 2x(3x) (2) (3x) (2)

6x2 10

12.3x2 4x 2

2x 3

12x 6 6x3 8x2 4x

17x2 6

A-20	Appendix II Polynomials

PRACTICE

Multiply.

13. (3x2)(4x3)

15. (3b2)( 2b)

17. ( 2x2)(3x3)

19. a 23 y5 b a 34 y2 b

21. 3(x 4)

23. 4(t 7)

25. 3x(x 2)

27. 2x2(3x2 x)

29. 2x(3x2 4x 7)

31. p(2p2 3p 2)

33. 3q2(q2 2q 7)

35. (a 4)(a 5)

37. (3x 2)(x 4)

39. (2a 4)(3a 5)

Square each binomial.

41. (2x 3)2

43. (2x 3)2

45. (5t 1)2

47. (9b 2)

Multiply.

49.(2x 1)(3x2 2x 1)

50.(x 2)(2x2 x 3)

51.(x 1)(x2 x 1)

52.(x 2)(x2 2x 4)

53.(x 2)(x2 3x 1)

14.	( 2a3)(3a2)
16.	(3y)( y4)
18.	( 7x3)( 3x3)
	2		4	3		2
20.	a		r b a		r b
		5		5
22.	3(a 2)
24.	6(s2 3)
26.	4y(y 5)
28.	4b3(2b2 2b)
30.	3y(2y2 7y 8)
32.	2t(t2 t 1)
34.	4v3( 2v2 3v 1)
36.	(y 3)(y 5)
38.	(t 4)(2t 3)
40.	(2b 1)(3b 4)

42. (2y 5)2

44. (2y 5)2

46. (6a 3)2

48. (7m 2)2

59.	4x 2	60.	6r 5
	3x 5		2r 3
61.	x2 x 1	62.	4x2	2x 1
	x 1			2x 1
63.	4x2 3x 4	64.	5r2	r 6
	3x 2			2r 1

APPLICATIONS

65.GEOMETRY Find a polynomial that represents the area of the rectangle (Hint: Recall that the area of a rectangle is the product of its length and width).

(x + 2) ft

(x − 2) ft

66.SAILING The height h of the triangular sail is 4x feet, and the base b is (3x 2) feet. Find a polynomial that represents the area of the sail.

(Hint: The area of a triangle is given by the formula

A 12 bh.)

4x ft

(3x − 2) ft

67.STAMPS Find a polynomial that represents the area of the stamp.

54.(x 3)(x2 3x 2)

55.(r2 r 3)(r2 4r 5)

56.(w2 w 9)(w2 w 3)

Multiply.
57. 4x 3		58. 5r 6
	x 2	2r 1

FIRST USA	(3x – 1) cm
CLASS

(2x + 1) cm

68.PARKING Find a polynomial that represents the total area of the van-accessible parking space and its access aisle.



(x + 10) ft		2x ft

69.TOYS Find a polynomial that represents the area of the Etch-A-Sketch.

(7x + 3) in.

(5x + 4) in.

70.PLAYPENS Find a polynomial that represents the area of the ﬂoor of the playpen.

(x + 6) in.

Appendix II Polynomials

A-21

WRITING

71.Explain how to multiply two binomials.

72.Explain how to ﬁnd (2x 1)2.

73.Explain why (x 1)2 x2 12. (Read as “is not equal to.”)

74.If two terms are to be added, they have to be like terms. If two terms are to be multiplied, must they be like terms? Explain.

REVIEW

75.THE EARTH It takes 23 hours, 56 minutes, and 4.091 seconds for the Earth to rotate on its axis once. Write 4.091 in words.

76.TAKE-OUT FOOD The sticker shows the amount and the price per pound of some spaghetti salad that was purchased at a delicatessen. Find the total price of the salad.

Joan's Spaghetti Salad

303 Foothill Plaza

Plaza Deli

0.783.95

NET WT. LB. PRICE/ LB. $

TOTAL PRICE $

77.Write 647 as a decimal.

78.Write 106 as a decimal.

79.Evaluate: 561.09 178 0.567

80.Evaluate: 679.4 ( 599.89)

81.Evaluate: 16 36

82. Find: 103.6 0.56

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	APPENDIX
Inductive and Deductive	III
Reasoning	III

Objectives

S E C T I O N III.1

1Use inductive reasoning to solve problems.

Inductive and Deductive Reasoning

2Use deductive reasoning to solve problems.

To reason means to think logically. The objective of this appendix is to develop your problem-solving ability by improving your reasoning skills. We will introduce two fundamental types of reasoning that can be applied in a wide variety of settings. They are known as inductive reasoning and deductive reasoning.

Self Check 1

Find the next number in the sequence 3, 1, 1, 3, . . . .

Now Try Problem 11

1 Use inductive reasoning to solve problems.

In a laboratory, scientists conduct experiments and observe outcomes. After several repetitions with similar outcomes, the scientist will generalize the results into a statement that appears to be true:

•If I heat water to 212°F, it will boil.

•If I drop a weight, it will fall.

•If I combine an acid with a base, a chemical reaction occurs.

When we draw general conclusions from speciﬁc observations, we are using inductive reasoning. The next examples show how inductive reasoning can be used in mathematical thinking. Given a list of numbers or symbols, called a sequence, we can often ﬁnd a missing term of the sequence by looking for patterns and applying inductive reasoning.

EXAMPLE 1 Find the next number in the sequence 5, 8, 11, 14, . . . .

Strategy We will ﬁnd the difference between pairs of numbers in the sequence.

WHY This process will help us discover a pattern that we can use to ﬁnd the next number in the sequence.

Solution

The numbers in the sequence 5, 8, 11, 14, . . . are increasing. We can ﬁnd the difference between each pair of successive numbers as follows:

8 5 3 Subtract the ﬁrst number, 5, from the second number, 8.

11 8 3 Subtract the second number, 8, from the third number, 11.

14 11 3 Subtract the third number, 11 from the fourth number, 14.

The difference between each pair of numbers is 3. This means that each number in the sequence is 3 greater than the previous one. Thus, the next number in the sequence is 14 3, or 17.

EXAMPLE 2 Find the next number in the sequence 2, 4, 6, 8, . . . .

Strategy The terms of the sequence are decreasing. We will determine how each number differs from the previous number.

WHY This type of examination helps us discover a pattern that we can use to ﬁnd the next number in the sequence.

A-23

A-24	Appendix III Inductive and Deductive Reasoning

Self Check 2

Find the next number in the sequence 0.1, 0.3, 0.5,0.7, . . . .

Now Try Problem 15

Self Check 3

Find the next letter in the sequence B, G, D, I, F, K, H, . . . .

Now Try Problem 19

Self Check 4

Find the next shape in the sequence below.

		. . .
,	,	,

Now Try Problem 23

Solution

Since each successive number is 2 less than the previous one, the next number in the sequence is 8 2, or 10.

	This number is			This number is		This number is
	2 less than the			2 less than the		2 less than the
	previous number.			previous number.		previous number.
2 ,		4	,	6	,	8	, . . . .

	EXAMPLE 3	Find the next letter in the sequence A, D, B, E, C, F, D, . . . .

Strategy We will create a letter–number correspondence and rewrite the sequence in an equivalent numerical form.

WHY Many times, it is easier to determine the pattern if we examine a sequence of numbers instead of letters.

Solution

The letter A is the 1st letter of the alphabet, D is the 4th letter, B is the 2nd letter, and so on. We can create the following letter–number correspondence:

Letter	Number
A	1	Add 3.
D	4	Add 3.
D	4
B	2	Subtract 2.
		Subtract 2.

E	5	Add 3.
		Add 3.

C	3	Subtract 2.
		Subtract 2.

		Add 3.
F	6


D	4	Subtract 2.
		Subtract 2.

The numbers in the sequence 1, 4, 2, 5, 3, 6, 4, . . . alternate in size. They change from smaller to larger, to smaller, to larger, and so on.

We see that 3 is added to the ﬁrst number to get the second number. Then 2 is subtracted from the second number to get the third number. To get successive numbers in the sequence, we alternately add 3 to one number and then subtract 2 from that result to get the next number.

Applying this pattern, the next number in the given numerical sequence would be 4 3, or 7. The next letter in the original sequence would be G, because it is the 7th letter of the alphabet.

EXAMPLE 4 Find the next shape in the sequence below.

. . .

Strategy To ﬁnd the next shape in the sequence, we will focus on the changing positions of the dots.

WHY The star does not change in any way from term to term.

Solution

We see that each of the three dots moves from one point of the star to the next, in a counterclockwise direction. This is a circular pattern.The next shape in the sequence will be the one shown here.

Appendix III

EXAMPLE 5 Find the next shape in the sequence below.

		. . .
,	,	,

Strategy To ﬁnd the next shape in the sequence, we must consider two changing patterns at the same time.

WHY The shapes are changing and the number of dots within them are changing.

Solution

Inductive and Deductive Reasoning

A-25

Self Check 5

Find the next shape in the sequence below.

. . .

Now Try Problem 27

The ﬁrst ﬁgure has three sides and one dot, the second ﬁgure has four sides and two dots, and the third ﬁgure has ﬁve sides and three dots.Thus, we would expect the next ﬁgure to have six sides and four dots, as shown to the right.

	2 Use deductive reasoning to solve problems.		B
As opposed to inductive reasoning, deductive reasoning moves from the general case
to the speciﬁc. For example, if we know that the sum of the angles in any triangle is
180°, we know that the sum of the angles of ^ABC shown in the right margin is 180°.			A	C
Whenever we apply a general principle to a particular instance, we are using deductive
reasoning.
	A deductive reasoning system is built on four elements:
1. Undeﬁned terms: terms that we accept without giving them formal meaning
2. Deﬁned terms: terms that we deﬁne in a formal way
3. Axioms or postulates: statements that we accept without proof
4. Theorems: statements that we can prove with formal reasoning
	Many problems can be solved by deductive reasoning. For example, suppose a
student knows that his college offers algebra classes in the morning, afternoon, and
evening and that Professors Anderson, Medrano, and Ling are the only algebra
instructors at the school. Furthermore, suppose that the student plans to enroll in a
morning algebra class. After some investigating, he ﬁnds out that Professor Anderson
teaches only in the afternoon and Professor Ling teaches only in the evening.Without
knowing anything about Professor Medrano, he can conclude that she will be his
algebra teacher, since she is the only remaining possibility.
	The following examples show how to use deductive reasoning to solve problems.
	EXAMPLE 6	Scheduling Classes An online college offers only one	Now Try Problem 31

calculus course, one algebra course, one statistics course, and one trigonometry course. Each course is to be taught by a different professor.The four professors who will teach these courses have the following course preferences:

1.Professors A and B don’t want to teach calculus.

2.Professor C wants to teach statistics.

3.Professor B wants to teach algebra.

Who will teach trigonometry?

Strategy We will construct a table showing all the possible teaching assignments.

Then we will cross off those classes that the professors do not want to teach.

State Flags

EXAMPLE 7

A-26	Appendix III Inductive and Deductive Reasoning

Self Check 7

USED CARS Of the 50 cars on a used-car lot, 9 are red, 31 are foreign models, and 6 are red, foreign models. If a customer wants to buy an American model that is not red, how many cars does she have to choose from?

Now Try Problem 35

WHY The best way to examine this much information is to describe the situation using a table.

Solution

The following table shows each course, with each possible instructor.

Calculus	Algebra	Statistics	Trigonometry

A	A	A	A
B	B	B	B
C	C	C	C
D	D	D	D

Since Professors A and B don’t want to teach calculus, we can cross them off the calculus list. Since Professor C wants to teach statistics, we can cross her off every other list. This leaves Professor D as the only person to teach calculus, so we can cross her off every other list. Since Professor B wants to teach algebra, we can cross him off every other list. Thus, the only remaining person left to teach trigonometry is Professor A.

Calculus	Algebra	Statistics	Trigonometry

A	A	A	A
B	B	B	B
C	C	C	C
D	D	D	D

The graph below gives the number of state ﬂags that feature an eagle, a star, or both. How many state ﬂags have neither an eagle nor a star?

Has an eagle			10
Has a star

			27
Has an eagle
Has an eagle			5
and a star			5

Strategy We will use two intersecting circles to model this situation.

WHY The intersection is a way to represent the number of state ﬂags that have both an eagle and a star.

Solution

In ﬁgure (a) on the following page, the intersection (overlap) of the circles shows that there are 5 state ﬂags that have both an eagle and a star. If an eagle appears on a total of 10 ﬂags, then the red circle must contain 5 more ﬂags outside of the

Appendix III Inductive and Deductive Reasoning

A-27

intersection, as shown in ﬁgure (b). If a total of 27 ﬂags have a star, the blue circle must contain 22 more ﬂags outside the intersection, as shown.

Eagle	Star	Eagle		Star
	5	5	5	22
5 flags have		5 + 5 = 10		5 + 22 = 27
both an eagle		flags have		flags have
and a star.		an eagle.		a star.
	(a)		(b)

From ﬁgure (a), we see that 5 5 22, or 32 ﬂags have an eagle, a star, or both. To ﬁnd how many ﬂags have neither an eagle nor a star, we subtract this total from the number of state ﬂags, which is 50.

50 32 18

There are 18 state ﬂags that have neither an eagle nor a star.

ANSWERS TO SELF CHECKS

1. 5 2. 0.9 3. M 4.

7. 16

A P P E N D I X III STUDY SET

VOCABULARY

Fill in the blanks.

1.reasoning draws general conclusions from speciﬁc observations.

2.reasoning moves from the general case to

the speciﬁc.

CONCEPTS

Tell whether the pattern shown is increasing, decreasing, alternating, or circular.

3.2, 3, 4, 2, 3, 4, 2, 3, 4, . . .

4.8, 5, 2, 1, . . .

5.2, 4, 2, 0, 6, . . .

6.0.1, 0.5, 0.9, 1.3, . . .

7.a, c, b, d, c, e, . . .

8.	,	,	. . .
,			,

9.ROOM SCHEDULING From the chart, determine what time(s) on a Wednesday morning a practice room

in a music building is available. The symbol X indicates that the room has already been reserved.

	M	T	W	Th	F

9 A.M.	X		X		X
10 A.M.	X	X			X
11 a.m.		X	X	X

10.COUNSELING QUESTIONNAIRE A group of college students were asked whether they were taking

amathematics course and whether they were taking an English course. The results are displayed below.

a.How many students were taking a mathematics course and an English course?

b.How many students were taking an

English course but	Mathematics		English
English course but	class		class
not a mathematics
course?
c. How many students	10	11	18
	10	11	18

were taking a mathematics course?

A-28	Appendix III Inductive and Deductive Reasoning

GUIDED PRACTICE

Find the number that comes next in each sequence.

See Example 1.

11.1, 5, 9, 13, . . .

12.11, 20, 29, 38, . . .

13.5, 9, 14, 20, . . .

14.6, 8, 12, 18, . . .

Find the number that comes next in each sequence.

See Example 2.

15.15, 12, 9, 6, . . .

16.81, 77, 73, 69, . . .

17.3, 5, 8, 12, . . .

18.1, 8, 16, 25, 33, . . .

29.			2			3	. . .
							. . .
30.	1	,		,			,
30.					. . .
		,	,		. . .
		,	,		,

What conclusion can be drawn from each set of information?

See Example 6.

31.TEACHING SCHEDULES A small college offers only one biology course, one physics course, one chemistry course, and one zoology course. Each course is to be taught by a different adjunct professor. The four professors who will teach these courses have the following course preferences:

1.Professors B and D don’t want to teach zoology.

2.Professor A wants to teach biology.

Find the letter that comes next in each sequence.

See Example 3.

19.E, I, H, L, K, O, N, . . .

20.C, H, D, I, E, J, F, . . .

21.c, b, d, c, e, d, f, . . .

22.z, w, y, v, x, u, w, . . .

Find the ﬁgure that comes next in each sequence.

See Example 4.

23.

. . .

24.

. . .

25.

. . .

26.

. . .

, , ,

Find the ﬁgure that comes next in each sequence.

See Example 5.

27.			. . .
			. . .
,	,	,	,

28.

. . .

3.Professor B wants to teach physics. Who will teach chemistry?

32.DISPLAYS Four companies will be displaying their products on tables at a convention. Each company will be assigned one of the displays shown below. The companies have expressed the following preferences:

1.Companies A and C don’t want display 2.

2.Company A wants display 3.

3.Company D wants display 1.

Which company will get display 4?


Display 1 Display 2					Display 3	Display 4

33.OCUPATIONS Four people named John, Luis, Maria, and Paula have occupations as teacher, butcher, baker, and candlestick maker.

1.John and Paula are married.

2.The teacher plans to marry the baker in December.

3.Luis is the baker.

Who is the teacher?

34.PARKING A Ford, a Buick, a Dodge, and a Mercedes are parked side by side.

1.The Ford is between the Mercedes and the Dodge.

2.The Mercedes is not next to the Buick.

3.The Buick is parked on the left end.

Which car is parked on the right end?

Use a circle diagram to solve each problem. See Example 7.

35.EMPLOYMENT HISTORY One hundred ofﬁce managers were surveyed to determine their employment backgrounds. The survey results are shown below. How many ofﬁce managers had neither sales nor manufacturing experience?

Sales experience	63

Manufacturing 47

experience

Both 16

36.PURCHASING TEXTBOOKS Sixty college sophomores were surveyed to determine where they purchased their textbooks during their freshman year. The survey results are shown below. How many students did not purchase a book at a bookstore or online?

Online 23

Bookstore 35

Both 6

37.SIBLINGS When 27 children in a ﬁrst-grade class were asked, “How many of you have a brother?” 11 raised their hands. When asked, “How many have a sister?” 15 raised their hands. Eight children raised their hands both times. How many children didn’t raise their hands either time?

38.PETS When asked about their pets, a group of 35 sixth-graders responded as follows:

•21 said they had at least one dog.

•11 said they had at least one cat.

•5 said they had at least one dog and at least one cat. How many of the students do not have a dog or a cat?

TRY IT YOURSELF

Find the next letter or letters in the sequence.

39.	A, c, E, g, . . .	40.	R, SS, TTT, . . .
41.	Z, A, Y, B, X, C, . . .	42.	B, N, C, N, D, . . .

Find the missing ﬁgure in each sequence.

43.

44.

Appendix III Inductive and Deductive Reasoning

A-29

Find the next letter in the sequence.

45.C, B, F, E, I, H, L, . . .

46.d, h, g, k, j, n, . . .

Find the next number in the sequence.

47.7, 9, 6, 8, 5, 7, 4, . . .

48.2, 5, 3, 6, 4, 7, 5, . . .

49.9, 5, 7, 3, 5, 1, . . .

50.1.3, 1.6, 1.4, 1.7, 1.5, 1.8, . . .

51.2, 3, 5, 6, 8, 9, . . .

52.8, 5, 1, 4 , 10 , 17, . . .

53.6, 8, 9, 7, 9, 10, 8, 10, 11, . . .

54.10, 8, 7, 11, 9, 8, 12, 10, 9, . . .

55.ZOOS In a zoo, a zebra, a tiger, a lion, and a monkey are to be placed in four cages numbered from 1 to 4, from left to right. The following decisions have been made:

1.The lion and the tiger should not be side by side.

2.The monkey should be in one of the end cages.

3.The tiger is to be in cage 4.

In which cage is the zebra?

56.FARM ANIMALS Four animals—a cow, a horse, a pig, and a sheep—are kept in a barn, each in a separate stall.

1.The cow is in the ﬁrst stall.

2.Neither the pig nor the sheep can be next to the cow.

3.The pig is between the horse and the sheep. What animal is in the last stall?

57.OLYMPIC DIVING Four divers at the Olympics ﬁnished ﬁrst, second, third, and fourth.

1.Diver B beat diver D.

2.Diver A placed between divers D and C.

3.Diver D beat diver C.

In which order did they ﬁnish?

58.FLAGS A green, a blue, a red, and a yellow ﬂag are hanging on a ﬂagpole.

1.The only ﬂag between the green and yellow ﬂags is blue.

2.The red ﬂag is next to the yellow ﬂag.

3.The green ﬂag is above the red ﬂag.

What is the order of the ﬂags from top to bottom?

A-30	Appendix III Inductive and Deductive Reasoning

APPLICATIONS

59.JURY DUTY The results of a jury service questionnaire are shown below. Determine how many of the 20,000 respondents have served on neither a criminal court nor a civil court jury.

Jury Service Questionnaire

997 Served on a criminal court jury

103 Served on a civil court jury

35Served on both

60.ELECTRONIC POLL For the Internet poll shown below, the ﬁrst choice was clicked on 124 times, the second choice was clicked on 27 times, and both the ﬁrst and second choices were clicked on 19 times.

How many times was the third choice, “Neither” clicked on?

Internet Poll

What would you do if gasoline reached $5.50 a gallon?

You may vote for more than one.

Cut down on driving

Buy a more fuel-efficient car Neither

Number of people voting

178

61.THE SOLAR SYSTEM The graph below shows some important characteristics of the nine planets in our solar system. How many planets are neither rocky nor have moons?

Rocky planets	4

Planets with moons	7

Rocky planets with moons	2

62.WORKING TWO JOBS Andres, Barry, and Carl each have a completely different pair of jobs from the following list: jeweler, musician, painter, chauffeur, barber, and gardener. Use the facts below to ﬁnd the two occupations of each man.

1.The painter bought a ring from the jeweler.

2.The chauffeur offended the musician by laughing at his mustache.

3.The chauffeur dated the painter’s sister.

4.Both the musician and the gardener used to go hunting with Andres.

5.Carl beat both Barry and the painter at monopoly.

6.Barry owes the gardener $100.

WRITING

63.Describe deductive reasoning and inductive reasoning.

64.Describe a real-life situation in which you might use deductive reasoning.

65.Describe a real-life situation in which you might use inductive reasoning.

66.Write a problem in such a way that the diagram below can be used to solve it.

20 10 30

APPENDIX

Roots and Powers

n	n	2	2n	n	3	3	n	n	2	2n	n	3	3
						2n							2n
1		1	1.000		1	1.000	51	2,601		7.141	132,651		3.708
2		4	1.414		8	1.260	52	2,704		7.211	140,608		3.733
3		9	1.732		27	1.442	53	2,809		7.280	148,877		3.756
4		16	2.000		64	1.587	54	2,916		7.348	157,464		3.780
5		25	2.236		125	1.710	55	3,025		7.416	166,375		3.803
6		36	2.449		216	1.817	56	3,136		7.483	175,616		3.826
7		49	2.646		343	1.913	57	3,249		7.550	185,193		3.849
8		64	2.828		512	2.000	58	3,364		7.616	195,112		3.871
9		81	3.000		729	2.080	59	3,481		7.681	205,379		3.893
10	100		3.162	1,000		2.154	60	3,600		7.746	216,000		3.915
11	121		3.317	1,331		2.224	61	3,721		7.810	226,981		3.936
12	144		3.464	1,728		2.289	62	3,844		7.874	238,328		3.958
13	169		3.606	2,197		2.351	63	3,969		7.937	250,047		3.979
14	196		3.742	2,744		2.410	64	4,096		8.000	262,144		4.000
15	225		3.873	3,375		2.466	65	4,225		8.062	274,625		4.021
16	256		4.000	4,096		2.520	66	4,356		8.124	287,496		4.041
17	289		4.123	4,913		2.571	67	4,489		8.185	300,763		4.062
18	324		4.243	5,832		2.621	68	4,624		8.246	314,432		4.082
19	361		4.359	6,859		2.668	69	4,761		8.307	328,509		4.102
20	400		4.472	8,000		2.714	70	4,900		8.367	343,000		4.121
21	441		4.583	9,261		2.759	71	5,041		8.426	357,911		4.141
22	484		4.690	10,648		2.802	72	5,184		8.485	373,248		4.160
23	529		4.796	12,167		2.844	73	5,329		8.544	389,017		4.179
24	576		4.899	13,824		2.884	74	5,476		8.602	405,224		4.198
25	625		5.000	15,625		2.924	75	5,625		8.660	421,875		4.217
26	676		5.099	17,576		2.962	76	5,776		8.718	438,976		4.236
27	729		5.196	19,683		3.000	77	5,929		8.775	456,533		4.254
28	784		5.292	21,952		3.037	78	6,084		8.832	474,552		4.273
29	841		5.385	24,389		3.072	79	6,241		8.888	493,039		4.291
30	900		5.477	27,000		3.107	80	6,400		8.944	512,000		4.309
31	961		5.568	29,791		3.141	81	6,561		9.000	531,441		4.327
32	1,024		5.657	32,768		3.175	82	6,724		9.055	551,368		4.344
33	1,089		5.745	35,937		3.208	83	6,889		9.110	571,787		4.362
34	1,156		5.831	39,304		3.240	84	7,056		9.165	592,704		4.380
35	1,225		5.916	42,875		3.271	85	7,225		9.220	614,125		4.397
36	1,296		6.000	46,656		3.302	86	7,396		9.274	636,056		4.414
37	1,369		6.083	50,653		3.332	87	7,569		9.327	658,503		4.431
38	1,444		6.164	54,872		3.362	88	7,744		9.381	681,472		4.448
39	1,521		6.245	59,319		3.391	89	7,921		9.434	704,969		4.465
40	1,600		6.325	64,000		3.420	90	8,100		9.487	729,000		4.481
41	1,681		6.403	68,921		3.448	91	8,281		9.539	753,571		4.498
42	1,764		6.481	74,088		3.476	92	8,464		9.592	778,688		4.514
43	1,849		6.557	79,507		3.503	93	8,649		9.644	804,357		4.531
44	1,936		6.633	85,184		3.530	94	8,836		9.695	830,584		4.547
45	2,025		6.708	91,125		3.557	95	9,025		9.747	857,375		4.563
46	2,116		6.782	97,336		3.583	96	9,216		9.798	884,736		4.579
47	2,209		6.856	103,823		3.609	97	9,409		9.849	912,673		4.595
48	2,304		6.928	110,592		3.634	98	9,604		9.899	941,192		4.610
49	2,401		7.000	117,649		3.659	99	9,801		9.950	970,299		4.626
50	2,500		7.071	125,000		3.684	100	10,000		10.000	1,000,000		4.642

A-31

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	APPENDIX
Answers to Selected Exercises	V

	Think It Through												(page 9)
1.	c		2.		b			3. e			4.	d		5.				a
	Study Set Section 1.1																		(page 10)
	Study Set Section 1.1																		(page 10)
1.	digits					3.		standard					5.				expanded						7.		inequality
9.																	P E R IO D S
							Trillions					Billions								Millions				Thousands			Ones
				trillions					billions						millions						thousands					Tens	Ones
					trillions						billions							millions				thousands				Tens	Ones
	Hundred					Trillions						Billions								Millions				ThousandsHundreds
	Hundred			Ten				Hundred	Ten			Hundred				Ten				Hundred	Ten
				Ten					Ten							Ten


				1 , 3 4 2 , 5 8 7 , 2 0 0 , 9 4 6
11.		a. forty						b. ninety						c. sixty-eight										d. ﬁfteen
13.

		0		1			2	3		4		5		6				7		8	9		10
15.

		0		1		2		3		4		5		6				7		8	9		10
		0		1		2		3		4		5		6				7		8	9		10

17.

19.
	0	1		2	3	4		5		6		7		8	9		10
21.	braces		23.			a.	3 tens				b.			7	c.	6 hundreds						d. 5
25.	a. 1 hundred million										b.			7 c.		9 tens			d.		4
27.	ninety-three					29. seven hundred thirty-two
31.	one hundred ﬁfty-four thousand, three hundred two
33.	fourteen million, four hundred thirty-two thousand, ﬁve
hundred 35. nine hundred seventy billion, thirty-one
million, ﬁve hundred thousand, one hundred four
37.	eighty-two million, four hundred ﬁfteen																			39.		3,737
41.	930	43.			7,021			45.			26,000,432					47.		200 40 5
49.	3,000 600 9							51.			70,000 2,000 500 30 3
53.	100,000 4,000 400 1
55.	8,000,000 400,000 3,000 600 10 3
57.	20,000,000 6,000,000 100 50 6
59.	a.		b.			61. a.							b.			63. 98,150
65.	512,970				67.	8,400				69.		32,400				71.		66,000
73.	2,581,000				75.		53,000; 50,000								77.		77,000; 80,000
79.	816,000; 820,000							81.			297,000; 300,000									83.		a. 79,590
b. 79,600			c.		80,000				d.		80,000				85. a. $419,160
b. $419,200					c. $419,000						d. $420,000						87.			40,025
89.	202,036				91.	27,598					93.			10,700,506				95.			Aisha
97.	a. the 1970s, 7							b. the 1960s, 9								c. the 1960s, 12
d. the 1980s
99.											Bar graph

ft)	225
cubic	200
cubic	175
(trillion	175
	150
	125

reserves	100
	75
	50
Gas	50
Gas	25
	U.S.	Venezuela Canada	Argentina	Mexico

		Line graph
	ft)	225
	ft)
	cubic	200
	cubic	175
	(trillion	175
		150
		125

	reserves	100
		75
		50
	Gas	50
	Gas	25
		25
		U.S. Venezuela Canada Argentina Mexico
101.	a.

7155

DATE March 9, 2010

Payable to	Davis Chevrolet		$	15,601.00

00 Fifteen thousand six hundred one and –––

100 DOLLARS

	Memo
	b.
				Aug. 12,	4251
			DATE	Aug. 12,	2010
	Payable to	DR. ANDERSON		$	3,433.00
					00
	Three thousand four hundred thirty-three and –––
					100 DOLLARS
	Memo
103.	1,865,593; 482,880; 1,503; 269; 43,449
105.	a. hundred thousands		b. 980,000,000; 9 hundred
millions 8 ten millions c. 1,000,000,000; one billion

	Study Set Section 1.2		(page 24)
1.	addend, addend, sum	3.	commutative 5. estimate
7.	rectangle, square 9.	square 11. a. commutative

property of addition b. associative property of addition


c. associative property of addition													d.	commutative
property of addition							13.		0		15.	plus			17.		33 plus 12
equals 45			19.	47, 52			21.			38	23.		689			25.		76			27.	876
29.	35	31.	92		33.		70		35.		75	37.		461			39.			8,937
41.	18,143		43.		1,810			45.		19		47.	33		49.			137			51.	241
53.	30	55.	60		57.		1,615			59.		1,207			61.		37,500
63.	1,020,000			65.		88 ft			67.		68 in.		69.			376 mi
71.	186 cm		73.		15,907				75.		56,460			77.		65			79.		979
81.	30,000		83.		121		85.		11,312			87.			50		89.			91 ft
91.	1,140 calories					93.		79,787,000 visitors									95.			597,876
97.	$28,800		99.		$6,645,000,000							101.			196 in.					103. 384 ft
109. a.		3,000 100 20 5									b. 60,000 30 7

A-33


A-34					Appendix V Answers to Selected Exercises
		Study Set Section 1.3														(page 36)

1.		minuend, subtrahend, difference																			3.	subtraction
5.		estimate					7.	4, 3, 7					9.			left, right					11.			minus
13.			83 30				15.			23		17.			61		19.			224		21.				303			23.		7,642
25.			2,562			27.		36			29.		48			31.			8,457			33.			6,483
35.			51,677			37.		44,444						39.			correct				41.			incorrect
43.			66,000			45.		50,000						47.			29		49.		37			51.			608
53.			1,048			55.		59			57.		2,901					59.		102		61.				20			63.		65
65.			30		67.	19,929						69.		197			71.			10,457				73.				303
75.			48,760			77.		110				79.			143,559					81.		19,299						83.		1,420 lb
85.			2,661 bulldogs								87.			1,495 mi						89. $55					91.			33 points
93.			1,764°F				95.			17 area codes									97.		$1,513					99.			a. $39,565
	b. $1,322					105.			a.		5,370,650						b.		5,370,000							c.		5,400,000
107.				52 in.		109. 5,530
		Study Set Section 1.4														(page 50)

	1. factor, factor, product 3. commutative, associative
5.		square				7. a. 4 8								b.		15 15 15 15 15 15 15
9.		a.		3	b.	5	11.				a. area					b. perimeter								c. area
	d. perimeter						13.				, , ( )					15.		A			l w or A								lw
17.			105		19.		272				21.		3,700				23.			750		25.				1,070,000
27.			512,000				29.			2,720				31.			11,200				33.		390,000
35.			108,000,000					37.				9,344				39.			18,368				41.			408,758
43.			16,868,238					45.				1,800				47.		135,000					49.			18,000
51.			400,000				53.			84 in.2					55.		144 in.2					57. 1,491
59.			68,948			61.		7,623					63.			0		65.		1,590				67.			44,486
69.			8,945,912				71.				374,644					73.			9,900			75.				2,400,000
77.			355,712				79.			166,500						81.		72 cups				83.				204 grams
85.			3,900 times					87.				63,360 in.							89.		77,000 words
91.			$73,645,500					93.				72 entries							95.		no			97.			18 hr
99.			$1,386 per night									101.				84 tablets					103.				54 ft2
105.				1,260 mi, 97,200 mi2											109. 20,642
		Study Set Section 1.5														(page 65)

	1. dividend, divisor, quotient; divisor, quotient, dividend;
	dividend, divisor, quotient															3. long					5.	divisible							7.	a. 7
	b. 5, 2				9.	a.	1		b. 6				c. undeﬁned								d. 0					11. a. 2					b. 6
	c.	3		d.	5	13.		37, 333						15.			a. 0, 5				b. 2, 3					c. sum
	d.	10		17.		,			,			19.		5, 9, 45					21. 4, 11, 44
23.			7		3	21		25.				6			12			72		27.		16			29.			29
31.			325		33.		218				35.		504				37.		602		39.			39 R 15
41.			21 R 33				43.			47 R 86						45.		19 R 132						47. 2, 3, 4, 5, 6, 10
49.			3, 5, 9			51.		none					53.			2, 3, 4, 5, 6, 10								55.			70		57.		22
59.			9,000			61.		50			63.		4,325					65.		6	67.			8 R 25					69. 160
71.			106 R 3				73.			509			75.			3,080				77.		5		79.			23 R 211
81.			30 R 13				83.			89		85.			7 R 1				87.		625 tickets
89.			27 trips				91. 2 cartons, 4 cartons														93.			9 times, 28 ounces
95.			14,500 lb				97.				$105				99.		5 mi			101.			13 dozen
103.				9 girls			105.				$4,344, $3,622, $2,996												111.				3,281
113.				1,097,334
		Study Set Section 1.6														(page 75)

1.		strategy				3.		subtraction									5.	multiplication										7.	addition
9.		multiplication									11.		division						13.		Analyze, Form, Solve,
	State, Check						15.				40		17.			$194,445					19.			179 episodes
21.			14 daily servings									23.			24 scenes						25.			26 full-size rolls,
	with one smaller roll left over																	27.		68 documents
29.			872,564 mi2					31.				$2,623 million									33.		20,360						35.		$462

37.	56 gal 39.	used: 54 GB, free: 26 GB		41. 426 ft
43.	10,080 min	45.	14 ﬁreplaces, 172 bricks left over
47.	179 squares	49.	$730 51. 23,778 mi	53. 8 $20-bills,

$4 change 55. 113 points 57.	388 ft2 63. Upward:
12,787. The sum is not correct.	65. Estimate: 4,200.
The product does not seem reasonable.


	Study Set Section 1.7													(page 87)
1.		factors			3.	prime				5. prime					7.			base, exponent
9. 45, 15, 9; 1, 3, 5, 9, 15, 45													11.		yes			13.		a. even, odd
b. 0, 2, 4, 6, 8, 10, 12, 14, 16, 18														c. 1, 3, 5, 7, 9, 11, 13, 15, 17, 19
15.		5, 6, 2; 2, 3, 5, 5							17.		2, 25, 2, 3, 5, 5								19.		a. base: 7,
exponent: 6						b. base: 15, exponent: 1												21.			1, 2, 5, 10
23.		1, 2, 4, 5, 8, 10, 20, 40										25.		1, 2, 3, 6, 9, 18								27.		1, 2, 4, 11,
22, 44			29.		1, 7, 11, 77						31.		1, 2, 4, 5,10, 20, 25, 50, 100
33.		2 4		35.		3 9			37.		7 7			39.		2 10 or 4 5								41.		2 3 5
43.		3 3 7			45. 2 3 9 or 3 3 6												47.		2 3 10 or 2 2 15
or 2 5 6 or 3 4 5										49.		1 and 11						51.		1 and 37					53. yes
55.		no, (9 11)					57.		no, (3 17)						59.			yes		61.			2 3 5
63.		3 13		65. 32 11							67.		2 34			69. 26					71.		3 72
73.		22 5 11				75.		2 3 17						77. 25				79.		54			81.		42(83)
83.		77 92			85.		a.	81			b.	64		87.		a.		32		b.		25			89.	a.	343
b.		2,187		91.		a.	9		b.		1	93. 90					95.		847			97.		225
99.		2,808		101.			1, 2, 4, 7, 14, 28, 1 2 4 7 14																			28
103. 22 square units, 32 square units, 42 square units
109. 125 band members
	Study Set Section 1.8													(page 98)

1.		multiples				3.	divisible						5. a. 12					b. smallest							7.	a. 20
b.		20	9.	a. two				b. two					c. one				d. 2, 2, 3, 3, 5, 180
11.		a. two			b. three					c. 2, 3, 108							13.		a. 2, 3, 5						b.	30
15.		a. GCF				b. LCM					17.		4, 8, 12, 16, 20, 24, 28, 32
19.		11, 22, 33, 44, 55, 66, 77, 88													21.		8, 16, 24, 32, 40, 48, 56, 64
23.		20, 40, 60, 80, 100, 120, 140, 160															25.		15			27.		24		29.	55
31.		28	33.		12		35.		30		37.			80	39.			150			41.		315			43.	600
45.		72	47.		60		49.		2		51.		3		53.		11		55.			15		57.		6
59.		14	61.		1		63.		1		65.		4	67.			36		69.		600, 20
71.		140, 14			73.		2,178; 22						75.		3,528; 1					77.		3,000; 5
79.		204, 34			81.		138, 23					83.		4,050; 1					85.		15,000 mi,
22,500 mi, 30,000 mi, 37,500 mi, 45,000 mi																				87.		180 min or 3 hr
89.		6 packages of hot dogs and 5 packages of buns
91.		12 pieces				93.		a. $7				b. 1st day: 4 students, 2nd day:
3 students, 3rd day: 9 students														99.			11,110				101.			15,250
	Study Set Section 1.9													(page 109)

1.		expressions					3.	parentheses, brackets													5.	inner, outer
7.		a. square, multiply, subtract													b. multiply, cube, add,
subtract				c. square, multiply										d. multiply, square

9. multiply, square 11. the fraction bar, the numerator and

the denominator						13.		quantity				15.		4, 20, 8				17.		9, 36, 16, 20
19.	47		21.	13		23.	38		25.		36		27.		24		29.		12
31.	a. 33 b.				15	33.		a.	43		b. 27			35.			100		37. 512
39.	64		41.	203		43.		73		45.		81	47.			3	49.		4	51.		6
53.	5		55.	16	57.		4	59.		5		61.	162				63.	27		65.		10
67.	3		69.	5,239		71.		15		73.		25		75.		22		77.		53	79.		2
81.	1		83.	25	85.		813		87.		49		89.		11		91.		191		93.		34
95.	323		97.		5	99.	14		101.			192		103.			74
105.		3(7) 4(4) 2(3), $43									107.		3(8 7 8 8 7), 114
109.		brick: 3(3) 1 1 3 3(5), 29;
aphid: 3[1 2(3) 4 1 2], 42

111.	22 32 52 72 4 9 25 49 87
113.	79° 115. 31 therms	117. 300 calories
119.	a. 125 b. $11,875	c. $95
125.	two hundred ﬁfty-four thousand, three hundred nine

	Chapter 1 Review						(page 113)
1.	6	2. 7	3.	1 billion			4.	8	5.	a. ninety-seven thousand,
two hundred eighty-three b. ﬁve billion, four hundred
forty-four million, sixty thousand, seventeen
6.	a.	3,207	b.		23,253,412			7.	500,000 70,000 300 2
8.	30,000,000 7,000,000 300,000 9,000 100 50 4
9.	0	1	2	3	4	5	6	7	8	9	10

10.

0 1 2 3 4 5 6 7 8 9 10

11.	12.		13. a. 2,507,300	b. 2,510,000
c. 2,507,350		d.	3,000,000 14. a.	970,000 b. 1,000,000
15.	a.		Bar graph

issued	15
issued	10
Permits	10
Permits	5
	5
	2001	2002	2003	2004	2005	2006	2007	2008
				Year

b.	Line graph

issued	15
issued	10
Permits	10
Permits	5
	5
	2001	2002	2003	2004	2005	2006	2007	2008
				Year


16.	Nile, Amazon, Yangtze, Mississippi-Missouri, Ob-Irtysh
17.	463		18.		18		19.	59		20.	1,018			21.		6,000			22.		50
23.	12,601			24.		152,169			25.		no	26.			14,661				27.	59,400
28.	a.	61 24 b. (9 91) 29										29.		227,453,217 passengers
30.	779,666				31.	$1,324,700,000						32.		2,746 ft					33.	61
34.	74		35.	217		36.		54	37.		505		38.		2,075				39.	incorrect
40.	12 8				20	41.		160,000			42.		3,041,092 square miles
43.	$13,445				44.	54 days				45.	423		46. 210					47.		720,000
48.	44,000			49.		9,263		50.		171,258				51.		1,580,344
52.	230,418				53.	2,800,000				54.		5 7			55.		a.	0	b. 7
56.	a. associative property of multiplication																		32 cm2
b.	commutative property of multiplication																57.
58.	6,084 in.2				59.		a. 2,555 hr				b.	3,285 hr					60.	330 members
61.	Santiago				62.		14,400 eggs				63.		18		64. 17				65.		37
66.	307		67.		23 R 27			68.		19 R 6			69.		0		70.		undeﬁned
71.	42 R 13				72.	380		73.		40 4		160			74.		It is not correct.
75.	It is divisible by 3, 5, and 9.										76.		4,000				77.		16, 25
78.	34 cars			79.		185°F			80. 383 drive-in theaters 81.												900 lb
82.	1,200 cars				83.		2,500 boxes				84. 68 hats, 12 yards of
thread left over						85. 147 cattle					86.		96 children						87. 1, 2, 3, 6,
9, 18		88. 1, 3, 5, 15, 25, 75								89. 2 10 or 4 5								90.		2 3 9

				Appendix V Answers to Selected Exercises																				A-35
or 3 3 6				91.		a. prime			b. composite									c. neither
d. neither				e. composite					f. prime						92.		a. odd				b. even
c. even			d.	odd			93.	2 3 7					94.		3 52				95.	22 5 11
96. 22 5 7					97. 64			98.	53 132					99.		125			100. 121
101.		784	102.			2,700		103.		9, 18, 27, 36, 45, 54, 63, 72, 81, 90
104.		a. 24, 48				b. 1, 2		105.			12			106.		12			107.		45
108.		36	109.			126	110.		360				111.		140			112.		84		113.		4
114.		3	115.		10		116.	15	117.					21	118.				28	119.			24
120.		44	121.			42 days		122.			a.		8 arrangements								b.	4 red
carnations, 3 white carnations, 2 blue carnations																					123.		45
124.		23	125.			243	126.		4		127.			32		128.			72		129.		8
130.		8	131.		1	132.		3	133.			28			134.		9		135.		77
136.		60
	Chapter 1 Test						(page 128)

1.	a. whole			b. inequality				c. value			d. area	e. divisible
f.	parentheses, brackets						g.	prime
2.	0	1	2	3	4	5	6	7	8	9

3. a. 1 hundred b. 0 4. a. seven million, eighteen thousand, six hundred forty-one b. 1,385,266

c.	90,000 2,000 500 60 1												5.	a.				b.
6.	a. 35,000,000				b.		34,800,000					c.	34,760,000
7.
			35
		of teams	30
			25
			20
		Number	20
			15
			10
			10
			5
				1960	1970			1980		1990		2000		2008
									Year
8.	248, 248 287					535			9.	225,164				10.		942			11.	424
12.		41,588		13.	72		14.		114 R 57, (73 114) 57											8,379
15.		13,800,000			16.	250			17.		43,000			18.			2,168 in.
19.		529 cm2		20. a. 1, 2, 3, 4, 6, 12									b. 4, 8, 12, 16, 20, 24
c.	8 5		21.	22 32 5 7					22.		32 teeth					23.		4,933 tails
24.		96 students			25.		4,085 ft2				26.		414 mi					27.	$331,000
28.		a. associative property of multiplication																b. commutative
property of addition							29.		a.	0		b.	0	c.		1		d. undeﬁned
30.		90	31.	72	32.		6	33.		4	34.		a.	40 in.				b. rice: 5
boxes, potatoes: 4 boxes 35. It is divisible by 2, 3, 4, 5, 6,
and 10.			36.	58	37.		29		38.		762		39.		44			40.	1

	Think It Through	(page 135)
$4,621, $1,073, $3,325
	Study Set Section 2.1 (page 139)

1.	Positive, negative	3.	graph 5.	absolute value
7.	a. 225 b. 10 sec		c. 3°	d. $12,000 e. 1 mi
9.	a. The spacing is not uniform.			b. The numbering is not

uniform. c. Zero is missing. d. The arrowheads are not

drawn.	11. a. 4 b. 2 13. a. 7 b. 8
15. a.	15 12 b. 5 4

A-36			Appendix V	Answers to Selected Exercises
17.
17.		Number		Opposite			Absolute value
		Number		Opposite			Absolute value

		25		25		25
		39		39		39
		0		0		0

19.	a. ( 8) b. 0 8 0 c. 8 8				d. 0 8 0
21.	a. greater, equal			b. less, equal
23.

		−5 −4 −3 −2 −1 0 1 2 3 4 5
		−5 −4 −3 −2 −1 0 1 2 3 4 5

25.

		−5		−4 −3			−2	−1 0				1		2	3		4		5
27.

		−5		−4 −3			−2	−1 0				1		2	3		4		5
		−5		−4 −3			−2	−1 0				1		2	3		4		5
29.

		−5		−4 −3			−2	−1 0				1		2	3		4		5
		−5		−4 −3			−2	−1 0				1		2	3		4		5
31.			33.				35.			37.				39.			true		41.			true
43.	false			45.		false			47.			9	49.		8		51.	14			53.		180
55.	11			57.	4		59.		102			61.	561			63.		20			65.		6
67.	253				69.	0		71.				73.				75.					77.
79.	52, 22, 12, 12, 52, 82													81.		3, 5, 7
83.	31 lengths						85. 0, 20, 5, 40, 120													87. peaks: 2, 4, 0;
valleys: 3, 5, 2									89.		a. 1 (1 below par)

b. 3 (3 below par) c. Most of the scores are below par.

91. a. 20° to 10°			b. 40° c. 10° 93. a. 200 yr
b. A.D. c. B.C. d.			the birth of Christ
95.	15°			Line graph
95.				Line graph


(Fahrenheit)	10°
	10°
	5°
	5°
Temperature	0°

		Mon. Tue. Wed. Thu. Fri.


	−5°
	−5°
	−10°
	−10°
	−15°
	−15°

105. 23,500 107. 761

109. associative property of multiplication

Think It Through (page 148)

decrease expenses, increase income, decrease expenses, increase income, increase income, increase income, decrease expenses, decrease expenses, increase income, decrease expenses


	Study Set Section 2.2										(page 152)
1.	like			3.	identity			5. Commutative
7.	a.		010 0			10, 0 12			0	12	b. 12		c.	2	9.	subtract,
larger			11.		a. yes			b.	yes	c. no d.			no	13. a.			0 b. 0
15.		18, 19				17.	5, 2		19.		9	21.	10	23.		62
25.		96		27.		379		29. 874				31. 3		33.	1
35.		22		37.		48	39.		357	41.		60	43.	7	45.		4

47.	10	49.	41	51.	3	53.	6 55.			3	57. 7
59.	9 61. 562			63.	2	65.	0	67.	0		69. 2		71. 1
73.	3	75. 1,032			77.	21		79.	8,348			81.	20
83.	112°F, 114°F			85.	a. 15,720 ft				b. 12,500 ft
87.	a. 9 ft		b.	2 ft above ﬂood stage						89.		195°
91.	5, 4% risk		93. 3,250 m				95.	($967)			103. a.		16 ft
b. 15 ft2		105. 2 53


	Study Set Section 2.3												(page 162)
1.	opposite, additive									3.	value				5.	opposite						7.		3
9.	change			11.			a.	3		b. 12				13.		, 6, 9
15.		a. 8 ( 4)						b. 4 ( 8)								17.			3, 2, 0
19.		2, 10, 6, 4						21. 7					23. 10						25.			9	27.		18
29.		18		31.		50			33.		a. 10				b.		10			35. a.			25			b. 25
37.		15		39.		9	41.			2		43.		10			45.			9		47.		12
49.		8	51.		0		53.		32		55.		26			57.			2,447				59.			43,900
61.		3	63.	10			65.	8		67.		5		69.		3		71.		1			73.		9
75.		22		77.		9	79.			4		81.		0		83.		18				85.		8
87.		25		89.		2,200 ft					91.		1,066 ft					93.			8
95.		4 yd			97.		$140				99.		Portland, Barrow, Kansas City,
Atlantic City, Norfolk										101. 470°F							103.			16-point increase
109. a.			24,090				b.	6,000				111.		156
	Study Set Section 2.4												(page 172)

1.	factor, factor, product										3.		unlike				5.		Associative
7.	positive, negative									9. negative						11.			unlike/different
13.		0	15.	a. 3			b. 12				17.		a. base: 8, exponent: 4
b. base: 7, exponent: 9											19. 6, 24							21.		15			23.			18
25.		72		27.		126				29.	1,665					31.		94,000						33.		56
35.		7	37.	156			39.		276			41.		1,947			43.			72,000,000
45.		90	47.		150		49.			384			51.		336					53. 48					55. 81
57.		36	59.		144		61.			27			63.		32			65.			625		67.			1
69.		49, 49			71. 144, 144								73.		60				75.			0	77.		64
79.		20		81.		18			83.		60		85.		48				87.		8,400,000
89.		625		91.		144			93.		1		95.		120				97.			2,000 ft
99.		a. high: 2, low: 3								b. high: 4, low: 6
101. a. 402,000 jobs										b. 423,000 jobs											c. 581,000 jobs
d. 528,000 jobs								103. 324°F							105.			$1,200
107. 18 ft					109. $215,718									115. 2, 3, 5, 7, 11, 13,
17, 19, 23, 29					117.			43 R 3
	Study Set Section 2.5												(page 180)

1. dividend, divisor, quotient; dividend, divisor, quotient
3.	by, of			5.	a. 5(5)					25				b. 6( 6)							36
c. 0( 15)					0		7.	a. positive						b. negative								9.	a.		0
b. undeﬁned						11.		a. always true								b. sometimes true
c. always true							13.	7			15.		4			17.		6			19.		8
21.		22		23.		39			25.		30			27.		50				29. 2				31.		5
33.		9	35.	4		37.		16		39.		21		41.			40		43.			500
45.		a. undeﬁned						b.	0		47.		a.	0		b. undeﬁned								49. 3
51.		17		53.		0	55.			5		57.		5			59.		undeﬁned
61.		19		63.		1	65.			20		67. 1					69.			10		71.		24
73.		30		75.		4		77. 542						79.		1,634						81.	$35 per
week			83.	1,010 ft						85.		7° per min							87.			6 (6 games
behind) 89. $15									91.		$17				99.		211			101.			associative
property of addition										103.		no

	Study Set Section 2.6																			(page 188)
1.	order				3.		inner, outer												5.		a. square, multiplication,
subtraction b. multiplication, cube, subtraction, addition
c. subtraction, multiplication, addition																											d. square,
multiplication 7. parentheses, brackets, absolute value
symbols, fraction bar															9. 4, 20, 20, 28													11. 8, 1, 5,
14				13.	10					15.				62					17.			15				19. 12			21.			12
23.		80			25.			72						27.				200					29.			4	31.		28			33.		17
35.		71		37.			21				39.			50				41.			6				43.		12		45.				a.	12
b.	5			47.	a.		60				b.			14				49.			2		51.				3	53.		770
55.		5,000					57.				7				59.				1		61. 17						63.	21				65.		19
67.		7			69.		12				71.				14				73.				11				75.	2	77.				5
79.		3			81.		5				83.				166				85.				0			87. 14			89.				112
91.		22		93.			8			95.		3						97.			400 points							99.		19
101. $8 million 103. It’s better to refer to the last four
years, because there was an average budget surplus of
$16 billion.							105.				a.			90 ft below sea level ( 90)																			b. $600
lost ( 600)							c. 400 ft											111.				a. 3					b. 4			113.				no
	Chapter 2 Review																(page 192)
	Chapter 2 Review																(page 192)
1. {. . . , 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, . . .}																													2.			a. $1,200
b. 10 sec							3.			33 ft
4.	a.

				−4 −3						−2				−1				0				1			2		3	4
				−4 −3						−2				−1				0				1			2		3	4
b.

			−4 −3 −2 −1												0				1			2				3	4
			−4 −3 −2 −1												0				1			2				3	4
5.	a.				b.					6.			a. false								b. true						7. a.		5		b.		43		c. 0
8.	a. 8					b. 8					c.	0				9. a. 12									b.		12	c. 0
10.		a. negative									b. the opposite														c. negative						d. minus
11.
11.				Position										Player															Score to par
				Position										Player															Score to par

					1									Helen Alfredsson																		12
					2									Yani Tseng																			9
					3									Laura Diaz																			8
					4									Karen Stupples																			7
					5									Young Kim																			6
					6									Shanshan Feng																			5

12.		a. 1998, $60 billion																b. 2000, $230 billion												c. 2004,
$420 billion								13.				10						14.			9				15. 32			16.		73				17.		0
18.		0		19. 8						20.				3				21.			10				22.		8	23. 4					24.			20
25.		76			26.			31						27.				374					28.			3,128		29.			a. 11
b. 4				30. a.				yes						b. yes						c. no						d. no		31.			a. 100 ft
b. 66 ft					32.				136°F						33.				opposite								34.	a. 9 ( 1)
b. 6 ( 10)										35.				3				36.				21				37. 4			38.			6
39.		112			40.					8				41.				37				42.				30	43.		16			44.		24
45.		4			46.		22				47.				6			48.			8				49.		62		50.			103
51.		75		52.			a. 77							b. 77							53.			225 ft				54.		180°, 140°
55.		44 points						56.				$80							57.			14				58. 376						59.		322
60.		25		61.			25					62.			204							63.			68,000,000
64.		30,000,000								65.				36					66.			36				67. 120				68. 100
69.		450			70.		48				71.				260, 390											72. 540 ft							73.		125
74.		32			75.			4,096						76.				256				77.				negative			78.				In the

ﬁrst expression, the base is 9. In the second expression, the

base is 9. 81, 81 79. 3, 5, 15	80.	The answer is
incorrect: 18( 8) 152 81. 5	82.	2 83. 8 84. 8

Appendix V Answers to Selected Exercises

A-37

85.		10		86. 1		87.		50		88.		400		89.		23	90.		17
91.		0		92.	undeﬁned				93.		32		94.		5	95. 2 min
96.		4,729 ft				97. 22				98.		4	99.		40	100.		8	101.		41
102.			0	103. 13				104.		32		105. 12				106. 16				107. 4
108.			34		109.		1		110. 4				111.		5	112. 55
113.			2,300		114.		2
	Chapter 2 Test							(page 201)
1.	a. integers					b. inequality						c. absolute value
d.	opposites					e. base, exponent							2.	a.			b.		c.
3.	a. true					true		c. false				d. false				e. true			4.	Poly
5.		−5 −4			−3	−2 −1 0 1 2 3 4 5
		−5 −4			−3	−2 −1 0 1 2 3 4 5
6.	a. 3				b.	145		c. 1			d. 32					. 3		7.	a. 13
b.	1			c.	191	d. 15				e. 150				8. a. 70				b. 292
c.	48			d. 54		e. 26,000,000						9. 5( 4)					20		10. a. 8
b. 8				c.	9	d. 34			e. 80				11.	a. 12				b.	18	c.	4
d. 80 12. a. commutative property of addition
b. commutative property of multiplication																	c. adding
13.		a. undeﬁned					b. 5				c.	0	d.	1	14.		a.	16	b. 16
15.		1		16.	27		17.		34		18.		88	19. 6			20. 48
21.		24			22.	58	23.		72°F				24.	$203 lost ( 203)
25.		154 ft			26. 350 ft					27.		15		28.		$60 million
	Chapters 1–2 Cumulative Review															(page 203)
1.	a.		7 millions				b.	3	c.	7,326,500					d.	7,330,000
2.	CRF Cable
3.				120								Bar graph
				120
				110
			U.S. nuclear power plants	100
		Number of operable		90
				80
				70
				60
				50
				40
				30
				20
				20
				10
						1978			1983		1988		1993		1998		2003		2008

Source: allcountries.org and The World Almanac and Book of Facts, 2009

4.	360		5.	1,854				6.			24,388				7.		3,806			8.	4,684		9.	37,777
10.		1,432		11.			no		12.				65 wooden chairs								13.	11,745
14.		5,528,166					15.		21,700,000							16. 864 tennis balls
17.		104 ft, 595 ft2							18.			25, 144, 10,000								19.	87 R 5		20.		13
21.		467	22.			28		23.				yes		24.		10 times, 20 ounces
25.		60 rolls				26.		1, 2, 3, 6, 9, 18									27. a. prime number, odd
number			b. composite number, even number c. neither,
even number							d. neither, odd number													28. 23 32 7
29.		114	30.			175			31.			24		32.		30		33.		6	34.	27	35.		38
36.		10	37.		2		38.			41 mph
39.		a.

			−3			−2		−1				0		1		2		3
			−3			−2		−1				0		1		2		3
b.

		−4 −3 −2 −1											0	1			2
		−4 −3 −2 −1											0	1			2
40.		3	41.			21		42.			$79			43.			273° Celsius
44.		$55,000					45.		37				46.		70			47.	3		48.	4
49.		129	50.			1		51.			23			52.		0		53.		4	54.	3
55.		100 ft				56.		$4,000,000

A-38					Appendix V					Answers to Selected Exercises
	Study Set Section 3.1												(page 216)															57.					1			1	1			1			1
																																	1			1	1			1			1
1.	fraction					3.	proper, improper								5.	equivalent																	2			3	4			5			6
7.	building					9.	equivalent fractions:									2			1										1				1			1	1			1			1
7.	building					9.	equivalent fractions:									6			3										1				1			1	1			1			1
11.		a. improper fraction										b. proper fraction										c. proper							2				4			6	8			10			12
11.		a. improper fraction										b. proper fraction										c. proper
fraction					d. improper fraction									13.		5		15.			numerators								1				1			1	1			1			1
		7			7																								3				6			9	12			15			18
17.			8	, 8		19.		3, 1, 3, 18				21. numerator: 4; denominator: 5
23. numerator: 17; denominator: 10																25.			3	,	1	27.			5,	3			1				1			1	1			1			1
			1	3		7		5											4		4				8	8			4				8			12	16			20			24
29.			4,	4	31. 12,			12		33.		a.	4	b. 1			c.		0		d. undeﬁned								1				1			1	1			1			1
35.		a. undeﬁned						b. 0			c. 1			d.	75		37.			35		39.			12				5				10			15	20			25			30
35.		a. undeﬁned						b. 0			c. 1			d.	75		37.			40		39.			27				5				10			15	20			25			30
41.			45		43.	4		45.		15		47.		22	49.			35			51.		48		53.		36		1				1			1	1			1			1
41.			54		43.	14		45.		30		47.		32	49.			28			51.		45		53.		9		6				12			18	24			30			36
55.			48		57.	15		59.		28		61.		a. no		b. yes						63.		a. yes					1			21				1				27
55.			8		57.	5		59.		2		61.		a. no		b. yes						63.		a. yes					1			21				1	65. 15			27		69. 1
			8			5				2																		59.	5		61. 128			63.		30			67.	64
b. no					2			4		69.		1	71.		1		73.			3		75.		in simplest				59.	5		61. 128			63.		30			67.	64	5		77
b. no				65.		67.				69.		3	71.		24		73.			8		75.		in simplest					8			3			2		25		2		5		77
					3			5				3			24					8								71.	3	73.		2	75.		9	77.	81	79.	3	81.	6	83.	60
form				77. in simplest form									79.		10		81.		5			83.		6				71.	3	73.		2	75.		9	77.	81	79.	3	81.	6	83.	60
form				77. in simplest form									79.		11		81.		9			83.		7				85.	1	87.		60 votes			89. 18 in., 6 in., and 2 in.
															11				9					7					2
85.			17		87.	5	89.			35	91.		1		93.					6		95.		8					2
85.			17		87.	5	89.			35	91.		1		93.					6		95.		8					3				1
			13			2				12				17						7					13			91.	8 cup sugar, 6 cup molasses
97.		not equivalent							99.		equivalent					101.				a.		32			5			91.	8 cup sugar, 6 cup molasses
97.		not equivalent							99.		equivalent					101.				a.		32		b.				93.	Inch						Growth Rate: June
																									32			93.	Inch						Growth Rate: June
																									32				1
103.			a.		16	b.	5	105.			a. 28, 22				b.		28				14		c.		22		11		1
103.			a.		16	b.	8	105.			a. 28, 22				b.		50				25		c.		50		25		5/6
							2	3																					2/3
107.			a.		20	b.	5, 5																						2/3
107.			a.		20	b.	5, 5																						1/2
109.												Office				117.				$2,307									1/2
109.												Office				117.				$2,307
												space																	1/3
																													1/3
																													1/6
										5
						Pediatrics ––																									Normal Nitrogen					Normal Nitrogen			Normal Nitrogen
										12																					Normal Nitrogen					Normal Nitrogen			Normal Nitrogen
														1																		House plants				Tomato plants				Shrubs
								Nurse’s				Lab		––
								Nurse’s				Lab		12															27 ft2				42 ft2		99. 9,646 mi2					3 in.
								station			Pharmacy																	95.	27 ft2			97.	42 ft2		99. 9,646 mi2			101.		3 in.
													––																											4
					Radiology									1
					Radiology			Orthopedics					12															109. 2			111.		23
						2		Orthopedics																				109. 2			111.		23
						––				3
						12				3
						12				––																		Study Set Section 3.3									(page 239)
										12																		Study Set Section 3.3									(page 239)

						Medical Center																							1. reciprocal						3.	quotient				5.		a. multiply, reciprocal
						Medical Center																									3
																													b. ,		3		7.	a. negative					b. positive						9.			a.			1		b.		1
																													b. ,				7.	a. negative					b. positive						9.			a.			1		b.		1
	Study Set Section 3.2												(page 228)																	2													7					8							1
																														2
																													11.	27, 27, 8, 9, 2, 4, 4, 9, 3										13.		a.				b.							c.

1. multiplication									3. simplify					5.	area		7. numerators,																										6							15					10
1. multiplication									3. simplify					5.	area		7. numerators,																8							1				3							14					35
denominators, simplify										9.		a. negative					b. positive												15.	a.			8	b. 14			c.			1		17.		3			19.				14		21.			35
denominators, simplify										9.		a. negative					b. positive												15.	a.				b. 14			c.					17.	16				19.				23		21.			8
c. positive					d. negative								base, height,						1	bh						4				11									63				16								23					8
										11.									1			13.		a.		4				3																			7						4
										11.									2			13.		a.	1				23.	3			25.	45 27. 320					29.		4		31.						7		33.				4
																			2						1				23.	4			25.	45 27. 320					29.		4		31.								33.				55
		3			7, 15, 2, 3, 5, 5, 24										1			1						14						4																		2							55
		3													1			1						14						3								5			2												5
b.				15.										17.		19.					21.
b.			1	15.										17.	8	19.		45			21.			27					35.				37.		50	39.			41.			43.			1			45.							47.		36
			1												8			45						27					35.	23			37.		50	39.	6		41.		3	43.			1			45.					8		47.		36
		24					4			35					9			5				1			1					23							6				3												8
		24					4			35					9			5				1			1					2					1				27						15							27						1
23.				25.					27.				29.			31.					33.			35.																								57.
23.		77		25.			15		27.		72		29.		8	31.		2			33.		2	35.				7	49.				51.			53.					55.														59.
		77					15				72				8			2					2					7	49.	15			51.		192	53.			8		55.				2										59.			64
		1			2					9				9							1				1					15					192				8						2						16							64
		1			2					9				9							1				1					3					8			13				2												11					15
37.				39.					41. a.				b.			43.	a.						b.
37.		10		39.	15				41. a.	25			b.	25		43.	a.				36		b.				216		61.				63.			65.				67.			69. 6								71.					73.
		10			15					25				25							36						216		61.	14			63.		15	65.	32			67.		9	69. 6								71.		6			73.		28
		15			9			49. 15 ft2						63 in.2			53. 6 m2								60 ft2					14					15		32					9											6					28
45.		15		47.								51.										55.										5
45.		32		47.								51.										55.							75.			5	77.		4 applications						79.		6 cups						81. a. 30 days
		32																											75.				77.		4 applications						79.		6 cups						81. a. 30 days
																														2

15 mi

c. 25 days

d. route 2

83. a. 16

in.

85. 7,855 sections 93.

is less than

95. Zero

120

97.

−2

−1

–4 = 4

−5 −4 −3 −2

−1

1 2 3 4 5

	Think It Through																											(page 251)
7
20
	Study Set Section 3.4																																		(page 252)
	Study Set Section 3.4																																		(page 252)
																							2
1.	common										3.					build,														5.					numerators, common, Simplify
1.	common										3.					build,											2			5.					numerators, common, Simplify
7.	larger								9.			9				11.						a.								once							b. twice														c. three times
7.	larger								9.			9				11.						a.								once							b. twice														c. three times																		1
13.		2, 2, 3, 3, 5, 180																			15.									7, 7, 14, 35, 14, 5, 19																											17.						5		19.				1
13.		2, 2, 3, 3, 5, 180																			15.									7, 7, 14, 35, 14, 5, 19																											17.					9			19.			2
		4									2												3														5													3												7						10
21.					23.											25.														27.														29.													31.								33.
21.		15			23.						5					25.												5		27.										21				29.						8							31.					11			33.			21
35.		9			37.						1					39.							13							41.							1					43.					1			45.											13				47.					3

		10									20												28														4										2															9								4
49.			19		51.						31					53.							24							55.							9							57.					3			59.								4		61.				11
49.		24			51.						36					53.							35							55.							20							57.					8			59.								5		61.				12
63.		7			65.				2			67.						11						69.									1				71.							22						73.							2					75.				11

		6							3									10															3											15													5									20
		3										1											23														5												341													9
77.									79.							81.																	83.											85.																			87.
77.				16					79.			4				81.							10										83.				12							85.					400														87.	20
89.		20					91.								23						93.									17					95.									1						97.							5					99.				17

			103													4														54															50												36										60
101. a.								7	in.					b.				3					in.							103.								11					in.						105.										a.		3
101. a.					32				in.					b.									in.							103.							16						in.						105.										a.	8
					32											32																					16																							8
b.		2				1			c.			17			of a pizza was left																															d. no											107.						1		lb,
b.		6			3				c.			24			of a pizza was left																															d. no											107.					16			lb,
		6			3							24																																																		16
undercharge												109.									7							of the full-time students study 2 or
undercharge												109.								10								of the full-time students study 2 or
more hours a day.																		111.												no					113.									a. RR: right rear
b. LR: left rear																														3							1										1							d. 2
																117.										a.									b.									c.
																117.										a.				8					b.			8						c.			32
	Study Set Section 3.5																																		(page 265)
	Study Set Section 3.5																																		(page 265)
																																					1°															7
1.	mixed								3.			improper																		5.				a.			5									b.			6										in.
1.	mixed								3.			improper																		5.				a.			5		3							b.			6						8				in.
7.	Multiply, Add, denominator																																				9.										4	,				2				,	1

																																															5					5					5
																																												1						5			4 3
11.			improper									13.							not reasonable: 4																														2																12
11.			improper									13.							not reasonable: 4																											5			2	7															12
15.			a. and, sixteenths																										b. negative, two																					17. 8, 4, 8, 4, 4,
4, 6, 6									19				, 2			3														34	, 1				9												13										104
					19.													21.																								23.										25.
					19.				8							8		21.												25					25							23.					2					25.									5
		68														26														1														3													2									1
27.									29.														31. 3														33.					5							35. 4													37.			10
27.				9					29.								3						31. 3									4					33.					5			5				35. 4									3				37.			10	2
																							2														1
39.		4			41.				2			43.						8												45.					3
39.		4			41.				2			43.						8							7					45.					3						3
47.												8											1														2							16						1
										−2 –											– –															1 –								–– = 3						–
												9											2														3							5						5

−5 −4 −3 −2 −1 0 1 2 3 4 5

				Appendix V					Answers to Selected Exercises														A-39
49.			10	= –3		1		98	3	= 1	1		1
			– ––			– – ––			–		–	3	–
			3			3		99	2		2	3	7

		−5 −4 −3 −2 −1 0 1 2 3 4 5
		1		2									4						9		1
51.	8		53.	7		55.		8	57.	10					59.		61.		6		63. 2
51.	8	6	53.	7	5	55.		8	57.	10					59.	9	61.		6	10	63. 2		3
		10				3				9			25				7				1
65.	1		67.			13		69.			71.						2		73.		2
65.	1	21	67.			13	4	69.		10	71.			9			2	9	73.		2	2

75.	12		77. 14							79. 2			81.		8	1	83.				35	85.		5
75.	12		77. 14							79. 2			81.		8	3	83.				72	85.	16
																3					72		16
			1							64			10				2					11				1
87.	1							89.				2			91.	a.	3				b.		93. 2
87.	1			4				89.		27		2		27	91.	a.	3	3			b.	3	93. 2			2
95.	a.		2			2		b.	1		1	97.	size 14, slim cut								99. 76		9		in.2
95.	a.		2					b.	1			97.	size 14, slim cut								99. 76		16		in.2
			3							3													16
101.		42			5		in.2		103.			64 calories			105.		357¢					$3.57
101.		42					in.2		103.			64 calories			105.		357¢					$3.57
			8
			1														1
107.		1				cups			109.			600 people			111.		8			furlongs
107.		1	4			cups			109.			600 people			111.		8		2	furlongs
115.		60						117.	4

	Think It Through																														(page 278)
workday: 6											2			hr; non-workday: 7																													5		hr;						3		hr
workday: 6											3			hr; non-workday: 7																													12		hr;					4			hr
											3																																12							4
	Study Set Section 3.6																																					(page 279)
	Study Set Section 3.6																																					(page 279)
1.	mixed										3.				fractions, whole																											5. carry													7.				a. 76,							3

																																																																		4
b.	76								3				9.		a.									12						b.			30							c.			18					d.				24						11.						21, 5, 5,
b.	76								4				9.		a.									12						b.			30							c.			18					d.				24						11.						21, 5, 5,
																		7															11																	3															1
35, 31, 35											13.				3													15.					6								17.				2										19.									3
35, 31, 35											13.				3				12									15.					6	15							17.				2					8					19.									3	6
21.		376					17						23.					714									19				25.				59						28				27.							132					29			29.							121			9
21.		376					21						23.					714													25.				59						45				27.							132								29.							121			10
							21																	20																	45														33															10
31.		147					8				33.				102											13					35.				129						28				37.							10				1				39.					13		8
31.		147					9				33.				102																35.				129						45				37.							10								39.					13		15
							9																	24																	45														4												15
					14																			43																4												23															1
41.		31									43.				71													45.					579										47.							62										49.					11
41.		31			33						43.				71								56					45.					579							15			47.							62				32						49.					11		30
				11											3																		7										2															7														5
51.		5							53.						9										55.						3				57.								5				59.								10									61.			397
51.		5		30					53.						9		10								55.						3		8		57.								5	3			59.								10				16					61.			397					12
							11											1																	1												1													5												1
63.		1											65.					7										67.				5									69.				6							71.						53								73.				2
63.		1					24						65.					7				2						67.				5				4					69.				6				3			71.						53					12			73.				2			2
75.		5					7				77.				3			5						79.							4		1		81.								461				1					83.						1		85.						5		1	hr
75.		5					8				77.				3									79.							4		3		81.								461				8					83.						4		85.						5			hr
							8											8															3														8											4									4
87.		7		1		cups							89.											20				1			lb				91.						108				1			in.							93.					2		3		mi
87.		7		6		cups							89.											20				16			lb				91.						108							in.							93.					2				mi
				6																								16																	2															4
95.		48			1			ft					97.					a. 20¢ per gallon																											b. 20¢ per gallon
95.		48			2			ft					97.					a. 20¢ per gallon																											b. 20¢ per gallon
				1																								3							1												3											4
99.		3				in.							105.							a. 4											b.				2								c.		4							d.			2
99.		3		4		in.							105.							a. 4									4		b.				2		4						c.		4		8					d.			2			5
	Study Set Section 3.7																																					(page 290)
	Study Set Section 3.7																																					(page 290)
1.	operations														3.										complex										5.							raising to a power
(exponent), multiplication, and addition
7.		2							1			b 1												2				9.				2			1								11.				23								13.					3, 6, 2, 2, 2, 5
		a
		a	3							10											15											3							5								4
		17													1																		7														1													13										2
15.									17.															19.											21.																	23.						5								25. 2
15.		20							17.							6								19.								26			21.											12						23.						5			30					25. 2					3
27.		26				1			29.						18									31.							5				33.							5			35.							5						37.								1
27.		26			4				29.						18									31.							32				33.						6				35.					18								37.								2

A-40														Appendix V Answers to Selected Exercises
			50													25																			27														1																			1
39.														41.											43.									1				45. 1																	47. 36													49.
39.			13											41.		26									43.									1		40		45. 1												3					47. 36													49.					3
			31																													5																											1									3
51.														53.		5					55. 14																57.					11							59.						1										61.
51.			45											53.		5					55. 14											24					57.					11							59.						1						6				61.						7
			3																		1														1							4													37
63.														65.		44									67.							8					69.										71.							1						73.								3
63.			10											65.		44					3				67.							8			2		69.					9					71.							1		70				73.								3
75.			8				4								77.				91				1			in.						79. yes										81.							3			1	hr									83. 9 parts
75.			8												77.				91							in.						79. yes										81.							3		4		hr									83. 9 parts
						15															4																														4
85.				7 full tubes;																		2		of a tube is leftover																											87.								7 yd2									89.						6 sec
85.				7 full tubes;																	3			of a tube is leftover																											87.								7 yd2									89.						6 sec
																					3
95.			2,248												97.						20,217													99.			1, 2, 3, 4, 6, 8, 12, 24
		Chapter 3 Review																																	(page 296)
		Chapter 3 Review																																	(page 296)
	1. numerator: 11, denominator: 16; proper fraction
2.			4		,	3								3.		The ﬁgure is not divided into equal parts.

			7			7
						2				2
4.									,							5.					a.				1						b.				0			c. 18											d. undeﬁned
4.						3			,					3		5.					a.				1						b.				0			c. 18											d. undeﬁned
6.			equivalent fractions:																													6					3					7.					12				8.						6								9.			21

																																8					4										18										16											45
10.				65										11.			45								12.					a. no										b. yes									13.								1		14.									5
10.			60											11.				9							12.					a. no										b. yes									13.								3		14.									12
15.			11											16.				9							17.					in simplest form																								18.								equivalent

			18													16
19.				7								,	17			20.						a. The fraction																					5			is being expressed as an
19.			24									,				20.						a. The fraction																				8				is being expressed as an
			24							24																																8
	equivalent fraction with a denominator of 16. To build the
	fraction, multiply																								5			by 1 in the form of																								2		.				b. The fraction																				4
	fraction, multiply																								8			by 1 in the form of																							2			.				b. The fraction																			6
																									8																										2																										6
	is being simpliﬁed. To simplify the fraction, remove the
	common factors of 2 from the numerator and denominator.
	This removes a factor equal to 1:																																											2					1.							21. numerators,
	This removes a factor equal to 1:																																																1.							21. numerators,
																																										2
	denominators, simplify																																		22.				5				2						23.					1					24.										14
	denominators, simplify																																		22.			6				3							23.					6					24.
																																						6				3												6														45
25.				5										26.							1				27.									21				28.							9				29.						1				30.						1			31.									9
25.			12											26.						25					27.										5			28.				4							29.						1				30.						1			31.									16
32.						125										33.									8									34.				4				35.							2 mi								36.							30 lb

										8																	125											9
37.				60 in.2												38.						165 ft2													39.				a.			8						b.							12								c.			1					d.			7
37.				60 in.2												38.						165 ft2													39.				a.			8						b.							11								c.		5						d.			8
				multiply, reciprocal																																		25																	7										6									30
40.																																			41.												42.												43.																44.
40.																																			41.			66									42.								8				43.						5										44.	7
45.								3						46.					8		47.														1			48. 1											49.							12 pins
45.														46.				5			47.													180				48. 1											49.							12 pins
						2												5																180
50.				30 pillow cases																										51.					5			52.				1							53.						5				54.									6

																																			7							2													4															5
55.				a.						5					b.			1			56.									2, 3, 3, 5, 90																	57.				5						58.								31

										8								5																																	6																40
			19													20																		23								7																	23									47
59.														60.											61.													62.											63.																64.
59.			48											60.				7							61.									36				62.				12							63.													6			64.							60
65.				7							in.					66.						3			67.								the second hour:																						3									2
65.				32							in.					66.					4				67.								the second hour:																						11									9
68.						1								69.				4			1				17

			250																		4									4
70.																		2												3							8	59											11
																–2 –													– –								–				–– = 2 ––
																		3												4							9	24											24

−5 −4 −3 −2 −1 0 1 2 3 4 5

71.	3	1					72.			3	11			73. 17							74.				2	1	75.					75			76.					11
71.	3	5					72.			3	12			73. 17							74.				2	3	75.							8	76.					5
	53								199								1								21													1
77.						78.							79.				2		80.								81.					40			82.	2				83. 16
77.	14					78.			100				79.				2	10	80.						22		81.					40			82.	2		2		83. 16
84.	40						4		85.		7		9				86.		6	2				87.		48		1	in.					88.		87 in.2
84.	40						5		85.		7		16				86.		6	9				87.		48			in.					88.		87 in.2
							5						16							9							8
89.	40 posters										90.					9 loads					91.				3	23				92.				6	1	93. 1						1
89.	40 posters										90.					9 loads					91.				3	40				92.				6	6	93. 1
																										40									6					12
94.	1	5					95.			255			19				96.		23		32				97.		83				1				98.	113				7

		16											20								35										18								20
			11											3										1								3								11
99.	31							100.			316						101.			20						102.				34					103.			39					gal
99.	31		24					100.			316				4		101.			20				2		102.				34			8		103.			39			12		gal
104.		5		in.					105.		8			106.					19		107. 8						8					108. 3						5

		8									9								72								15											8
			12										26								2						63									23
109.									110.								111.								112.									113.		2
109.					17				110.				29				111.					5			112.		17							113.		2	40
114.		14				1			115.				8	1			116.			11			1
114.		14				16			115.				8	3			116.			11
						16								3							6
117.		5 full tubes,											9			of a tube is left over																118. 8 in.
117.		5 full tubes,										10				of a tube is left over																118. 8 in.

	Chapter 3 Test																		(page 311)
1.		a. numerator, denominator																												b. equivalent												c. simplest
d.		simplify										e. reciprocal													f. mixed										g. complex
2.		a.			4			b.			1		3.				13				2		1
2.		a.		5				b.			5		3.			6					2
				5							5					6					6
4.							−1		1		−		2			7			1							4
									–				–			– = 1 –											–
									7				5			6			6					2 5

			−2					−1					0			1					2					3
5.		yes				6.			21				7.				a.		0		b. undeﬁned																8.	a.			3				b.		2

									24																																4						5
9.		5		10.							3			11.					6		12.					11						13.		11				14.			1			15.				9

		8										20														20								7							3							10
											47										1							39										1										5
16.		40				17.								18.						a.	9					b.								19.			261				20.						37
16.		40				17.					50			18.						a.	9	6				b.		21						19.			261		6		20.						37	12
				2																				1																			1
21.		1				22.						a. Foreman, 39															lb					b.		Foreman, 5											in.
21.		1		3		22.						a. Foreman, 39													2		lb					b.		Foreman, 5									2		in.
c. Ali,						1		in.			23.				8				24.		$1			1		million								25.				11		3	in.
c. Ali,						4		in.			23.			9					24.		$1			2		million								25.				11			in.
						4								9										2														4
26.		perimeter: 53												1				in., area: 106										2			in.2			27.				60 calories
26.		perimeter: 53												3				in., area: 106										3			in.2			27.				60 calories
														3														3
		12 servings																	13							3								20									5
28.														29.							30.											31.						32.
28.														29.					24		30.					10						31.				21		32.								3
33.		When we multiply a number, such as																																			3	, and its

																																					4
reciprocal,										4	, the result is 1:													3					4					1			34. a. removing
reciprocal,									3		, the result is 1:													4				3						1			34. a. removing
a common factor from the numerator and denominator
(simplifying a fraction)																					b. equivalent fractions
c. multiplying a fraction by a form of 1 (building an
equivalent fraction)
	Chapters 1–3 Cumulative Review																																					(page 313)
	Chapters 1–3 Cumulative Review																																					(page 313)
1.		a.		5				b. 8 hundred thousands																									c.	5,896,600
d.	5,900,000												2.	hundred billions																			3. Orange, San Diego,
Kings, Miami-Dade, Dallas, Queens																																		4.			a.	450 ft
b.		11,250 ft2											5.	30,996							6.			16,544, 16,544 3,456																							20,000
7.		2,400 stickers														8.			299,320							9.						991, 991 35											34,685

10.	$160			11. 1, 2, 3, 4, 6, 8, 12, 24													12.				2 32 52					13. 80
14.	21			15.	35		16.		$156,000							17.			{. . . , 5, 4, 3, 2,
1, 0, 1, 2, 3, 4, 5, . . .}									18.			true				19.			15				20.		10
21.	200 ft				22.		11°F per hour										23.				16		24. 35
25.	1		26. 2		27.			3	28.			5		29.						4	30.			4	31.		1	5
25.	1		26. 2		27.				28.			2		29.							30.		9		31.		1
							4					2							5				9				12
			1									11									5						53
32.				33. 30 sec					34.						in.		35.				10		36.
32.			35	33. 30 sec					34.				16		in.		35.				10	7	36.				8
	2				9				11								11
37.	7			38.	6		39. 9							40.		5					41. width: 28 in.,
37.	7	5		38.	6	10	39. 9				12			40.		5		15			41. width: 28 in.,
height: 6 in.							274		1	gal						3	5		ft						3		5
					42.									43.							44.						45.
					42.				4					43.			12				44.				64		45.		6
46.			2

			49

	Study Set Section 4.1								(page 325)
1. point			3.	expanded			5.		Thousands, Hundreds, Tens,
Ones, Tenths, Hundredths, Thousandths, Ten-thousandths
7. a. 10			b.	1	9.	a.	7	, 0.7		b.	47	, 0.47
				10			10
										100
11.		Whole-number part, Fractional part											13.	ths
15.		79,816.0245			17.	a.	9 tenths			b. 6			c. 4	d. 5 ones
19.		a. 8 millionths				b.	0		c. 5	d. 6 ones

21.30 7 10 100

23.		100 20 4								5			7				5
23.		100 20 4							10				100			1,000
									10				100			1,000
25.		7,000 400 90 8												6				4			6		8
25.		7,000 400 90 8															100			1,000
													10				100			1,000		10,000
27.		6		4			9				4						1

				10		1,000						10,000				100,000
							3
29.		three tenths,
29.		three tenths,						10
31.		ﬁfty and forty-one hundredths, 50																	41	33.		nineteen and

																			100
ﬁve hundred twenty-nine thousandths, 19																				529
ﬁve hundred twenty-nine thousandths, 19
																			1,000
																							3
35.		three hundred four and three ten-thousandths, 304
35.		three hundred four and three ten-thousandths, 304																						10,000
37.		negative one hundred thirty-seven hundred-thousandths,
		137			39.		negative one thousand seventy-two and four

	100,000
hundred ninety-nine thousandths, 1,072																				499		41.	6.187
hundred ninety-nine thousandths, 1,072																				1,000		41.	6.187
																				1,000
43.		10.0056 45. 16.39											47.		104.000004 49.								51.
53.				55.			57.				59.
61.				–3.9 –3.1						–0.7			0.8						4.5

			−5 −4 −3 −2 −1 0 1 2 3 4 5
63.			–4.25 –3.29 –1.84 –1.21													2.75

			−5 −4 −3 −2 −1 0 1 2 3 4 5
65.		506.2			67.		33.08				69.		4.234				71.		0.3656			73. 0.14
75.		2.7			77.		3.150				79.		1.414213						81.	16.100
83.		290.30350					85.		$0.28				87.		$27, 842					89. 0.7
91.		$1,025.78

Appendix V Answers to Selected Exercises

A-41

93.
	.1	.2	.3	.4	.5	cc
95. two-thousandths,		2	1	97.	$0.16, $1.02, $1.20,
95. two-thousandths,		1,000	500	97.	$0.16, $1.02, $1.20,
$0.00, $0.10 99. candlemaking, crafts, hobbies, folk dolls,
modern art	101. Cylinder 2, Cylinder 4					103. bacterium,
plant cell, animal cell, asbestos ﬁber				105. a. $Q3, 2007; $2.75
b. Q4, 2006; $2.05		113.	a. 12 1 in.		b.	9 5 ft2
			2			8


	Study Set Section 4.2		(page 339)
1. addend, addend, addend, sum				3.	minuend,
subtrahend, difference		5.	estimate		7. It is not correct:
15.2 12.5 28.7 9.		opposite		11.	a. 1.2	b. 13.55
c. 7.4 13. 46.600, 11.000			15.	39.9	17. 8.59	19. 101.561


21.	202.991		23.		3.31		25.		2.75			27.		341.7		29.		703.5
31.	7.235	33.		43.863			35.		14.7				37. 18.8					39. 14.68
41.	6.15	43.		66.7			45.		45.3					47.	6.81		49.		17.82
51.	4.5	53. 3.4					55.	790			57.		610		59.	10.9
61.	16.6	63.		38.29			65.		55.00				67. 47.91			69.			658.04007
71.	0.19	73.	4.1		75.		288.46				77.		70.29		79.		14.3
81.	57.47		83.		8.03		85.		15.2			87.		4.977		89.		2.598
91.	$815.80, $545.00, $531.49								93.			1.74, 2.32, 4.06; 2.90, 0, 2.90
95.	2.375 in.		97.		42.39 sec				99.		$523.19, $498.19								101.	1.1°,
101.1°, 0°, 1.4°, 99.5° 103.								20.01 mi						105. a. $101.94
b. $55.80					73		1	13				23			1		48		1	23
		113.		a.						b.				c.		d.
						60		60				60			3		25			25


	Study Set Section 4.3													(page 353)
1. factor, factor, partial product, partial product, product
3.	a.		2.28		b.		14.499				c.	14.0			d. 0.00026				5.		a. positive
b. negative						7.		a. 10, 100, 1,000, 10,000, 100,000														b. 0.1,
0.01, 0.001, 0.0001, 0.00001													9.		29.76		11.	49.84				13.		0.0081
15.		0.0522			17.			1,127.7				19.		2,338.4			21.		684		23.		410
25.		6.4759			27.			0.00115				29.			14,200,000			31.		98,200,000,000
33.		1,421,000,000,000									35.		657,100,000,000						37. 13.68
39.		5.28		41.			448,300				43.		678,231				45.		11.56			47.		0.0009
49.		3.16			51.		68.66			53.		119.70				55.	38.16			57.		14.6
59.		15.7			61.		250		63.		66.69				65. 0.1848					67.		1.69
69.		0.84			71.		0.00072				73.		200,000				75.		12.32
77.		17.48				79. 0.0049						81.			14.24		83.	8.6265
85.		57.2467						87.	22.39					89.		3.872			91.		24.48
93.		0.8649					95. 0.01, 0.04, 0.09, 0.16, 0.25, 0.36, 0.49, 0.64, 0.81
97.		1.9 in			99.			$74,100			101.				$95.20, $123.75
103.			0.000000136 in., 0.0000000136 in., 0.00000004 in.
105.			a.	2.1 mi				b.	3.5 mi				c.		5.6 mi		107.		$102.65
109.			a.	19,600,000 acres								b.		6,500,000,000
c.	3,026,000,000,000 miles												111.			a. 192 ft2			b.		223.125 ft2
c.	31.125 ft2						113.		a. $12.50, $12,500, $15.75, $1,575
b. $14,075					115. 136.4 lb								117.			0.84 in.		125.			22 5 11
127.			2 34
	Think It Through										(page 368)

1.	2.86

A-42							Appendix V Answers to Selected Exercises
		Study Set Section 4.4																											(page 368)
		Study Set Section 4.4																											(page 368)
1.		divisor, quotient, dividend																												3.			a.			5.26						b.		0.008
																																			10
5.		a.		13 106.6											b.		371						1669.5							7.					10		9.					thousandths
5.		a.		13 106.6											b.		371						1669.5							7.				10			9.					thousandths
																																		10
11.			a. left								b. right										13.						moving the decimal points in the
	divisor and dividend 2 places to the right																																							15.				2.1				17.			9.2
19.			4.27						21.				8.65				23.								3.35					25.				4.56					27.					0.46
29.			0.39						31.				19.72								33.						24.41						35.			280 70										28 7					4
37.			400 8										50				39. 4,000 50																			400 5									80
41.			15,000 5													3,000									43.				4.5178								45.			0.003009								47.			12.5
49.			545,200									51.				8.62											53.			4.04						55.			20,325.7
57.			0.00003												59.		5.162												61.				0.1				63.			3.5					65.			58.5
67.			2.66						69.				7.504								71.						0.0045							73.			0.321							75.			1.5
77.			122.02										79.				2.4										81.			9.75						83.			789,150								85. 0.6
87.			13.60							89.					0.0348										91.			1,027.19									93.			0.15625
95.			280 slices												97.			2,000,000 calculations																						99.					500 squeezes
101.				11 hr, 6 P.M.													103. 1,453.4 million trips																											105.				0.231 sec
113.				a.		5				b.			50
		Study Set Section 4.5																											(page 382)
		Study Set Section 4.5																											(page 382)
1.		equivalent											3.			terminating														5.							7.		zeros						9.		repeating
11.			a. 0.38								b.				0.212								13. a.								7				b.			77		15.					0.5
11.			a. 0.38								b.				0.212								13. a.							10					b.		100			15.					0.5
17.			0.875							19.					0.55						21.						2.6			23.				0.5625						25.					0.53125
27.			0.6			29.						0.225							31.						0.76							33.		0.002						35.				3.75
			12.6875																								0.583																			0.016
37.			12.6875									39.				0.1						41.					0.583							43.			0.07						45.			0.016
																													0.23					53. 0.49													1.85
47.			0.45							49.					0.60										51.				0.23					53. 0.49										55.			1.85
57.			1.08							59.					0.152										61.			0.370
63.																														3
																															1 –
							–3.83												–0.75								0.6				1 –
							–3.83												–0.75								0.6			4

					−5 − 4 −3 −2 −1 0 1 2 3 4 5
65.																	4
																–1–
									–3.5								5								0.2											3.875

					−5 − 4 −3 −2 −1 0 1 2 3 4 5
67.						69.									71.										73.								75.			6.25,					19		, 6		1
67.						69.									71.										73.								75.			6.25,				3			, 6		2
				8		6																			37								19							3
77.						,				, 0.81							79.												81.								83.							85.			1
77.					9	,		7		, 0.81							79.								90				81.				60				83.			22				85.			1
87.			0.57						89.				5.27				91.								0.35					93.				0.48						95.					2.55
97.			0.068							99.					7.305							101.						0.075						103.					0.0625, 0.375,
0.5625, 0.9375																			105.		3			in.					107. 23.4 sec, 23.8 sec, 24.2 sec,
0.5625, 0.9375																			105.	40				in.					107. 23.4 sec, 23.8 sec, 24.2 sec,
	32.6 sec					109.								93.6 in2											111.					$7.02						119.						a. {0, 1, 2, 3, 4, 5,
6, 7, 8, 9}									b. {2, 3, 5, 7, 11, 13, 17, 19, 23, 29}																																		c. {. . ., 3, 2,
1, 0, 1, 2, 3, . . .}
		Study Set Section 4.6																											(page 391)
		Study Set Section 4.6																											(page 391)
1.		square								3.				radical									5.				perfect							7.				a. 25, 25								b.			1	,		1
1.		square								3.				radical									5.				perfect							7.				a. 25, 25								b.			16	,	16
9.		a.		7			b.			2					11.		a.				1					b.		0				13. Step 2: Evaluate all
	exponential expressions and any square roots.
15.																–
15.																–		3																7

					−5 − 4 −3 −2 −1 0 1 2 3 4 5
17.			a. square root																b. negative														19.				7, 8							21.			5 and 5
23.			4 and 4												25.		4					27. 3								29.				12					31.				7				33. 31


35.	63		37.		2	39.			4	41.		1	43.	0.8	45.		0.9
				5					3			9
47.	0.3		49. 7			51.		16		53.	16		55.	3	57.		20
59.	140			61.		48			63. 43		65.		75	67.	7		69. 1
71.	10		73.				7	75.		140		77. 9.56			79.	1.4

							20
81.	15		83.	7		85.		1, 1.414, 1.732, 2, 2.236, 2.449, 2.646,
2.828, 3, 3.162						87.		3.87		89.	8.12		91.	4.904		93. 3.332
95.	a. 5 ft			b.		10 ft		97.		127.3 ft			99.	42-inch screen
109.		82.35		111.			39.304

	Chapter 4 Review																			(page 395)
							67
							67
1.	a. 0.67,												b.
1.								100					b.
								100																										0.8
																																		0.8
2.	a.		7 hundredths														b. 3							c. 8					d. 5 ten-thousandths
3.	10 6								4							5							2								3					4.			two and three

									10						100						1,000									10,000
tenths, 2						3			5.			negative six hundred ﬁfteen and ﬁfty-nine
tenths, 2						10			5.			negative six hundred ﬁfteen and ﬁfty-nine
						10
hundredths, 615														59				6.					six hundred one ten-thousandths,

														100
601						7. one hundred-thousandth,																												1						8.		100.61
10,000						7. one hundred-thousandth,																											100,000							8.		100.61
9.	11.997						10.				301.000016														11.						12.							13.					14.
15.										–2.7 –2.1 –0.8															1.55

				–5			–4 –3 –2 –1														0				1			2			3			4			5
16.		a. true								b. false									c.			true					d. true									17.		4.58
18.		3,706.082									19.					0.1					20.					88.1								21.			6.7030
22.		11.3150								23.				0.222228											24.			0.63527								25.				$0.67
26.		$13					27. Washington, Diaz, Chou, Singh, Gerbac
28.		Sun: 1.8, Mon: 0.6, Tues: 2.4, Wed: 3.8																																		29.				66.7
30.		45.188							31.				15.17					32.							28.428						33.					1,932.645
34.		24.30					35.				7.7							36.					3.1			37.					4.8						38.			29.09
39.		25.6							40.		4.939							41.						a.		760					b. 280							42.				10.75 mm
43.		$48.21							44.				8.15 in.								45. 15.87													46.		197.945
47.		0.0068							48.				2,310					49.							151.9									50.		0.00006
51.		90,145.2								52.				0.002897											53.			0.04						54.			0.0225
55.		10.61								56.			25.82								57.				0.0001089											58.		115.741
59.		a. 9,600,000 km2																	b.		2,310,000,000															60.			a.		1,600
b.	91.76						61.			98.07						62.					$19.43							63.							0.07 in.					64.			68.62 in.2
65.		9.3					66.			10.45						67.					1.29					68.					41.03					69.				6.25
70.		0.053					71.				63					72. 0.81										73. 0.08976												74.			0.00112
75.		876.5					76.				770,210										77.				4,800 40												480 4						120
78.		27,000 9											3,000								79.				12.9						80. 776.86											81. 13.95
82.		20.5					83.			$8.34								84.				0.51 ppb										85. 14 servings
86.		9.5 revolutions														87.					0.875							88. 0.4									89.				0.5625
		0.06																													3.056												95. 0.58
90.		0.06					91.			0.54						92. 1.3										93.					3.056					94.				0.57			95. 0.58
		1.03																								0.3,					10
96.							97.							98.									99.								10			, 0.3
96.							97.							98.									99.								33			, 0.3
																															33
100.																		9													3
																		– ––													2 –
										–3.3								– ––							1.125						2 –
										–3.3								10							1.125						4

					−5 −4 −3 −2 −1 0 1 2 3 4 5
101.			11				102.				307							1			7				103.						6.24						104.				0.175
101.			15				102.				300							1							103.						6.24						104.				0.175
			15								300							300
105.			93				106. 7.305												107. 34.88 in.2															108.				$22.25
109.			5 and 5								110. 7, 7												111.					7			112. 4									113.			10

								8						1
114.	0.3		115.						116. 0.9 117.							118. 0
114.	0.3		115.				13		116. 0.9 117.						6	118. 0
119.
119.				–	16				– 2				3	9

		−5 −4 −3 −2 −1 0 1 2 3 4 5
120.	a.		4.36 b.					24.45			c.	3.57	121. 30				122.	70
123.	27				124.			18	1	125.		70	126. 440				127.	8
123.	27				124.			18	3	125.		70	126. 440				127.	8
128.	33 in.					129. 9 and 10						130.	Since (2.646)2					7.001316,
we cannot use an									symbol.

	Chapter 4 Test																	(page 408)
1.		a. addend, addend, sum																						b. minuend, subtrahend,
difference											c. factor, factor, product																							d. divisor, quotient,
dividend									e.			repeating									f.		radical
2.		79			, 0.79							3.			a. 1 thousandth														b. 4								c.			6		d.			2 tens
2.		100			, 0.79							3.			a. 1 thousandth														b. 4								c.			6		d.			2 tens
4.		Selway, Monroe, Paston, Covington, Cadia																																								5. 4,519.0027
6.		a. 60 2												5				5			, sixty-two and ﬁfty-ﬁve hundredths,
6.		a. 60 2												10					100		, sixty-two and ﬁfty-ﬁve hundredths,
62		55							b.			8						1										3					, eight thousand
62	100								b.			100					10,000																, eight thousand
	100											100					10,000						100,000
thirteen one hundred-thousandths,																														8,013										7.			a.	461.7
thirteen one hundred-thousandths,																													100,000											7.			a.	461.7
b.	2,733.050												c. 1.983373										8. $0.65													9.			10.756
10.		6.121						11.						0.1024						12.			0.57					13.						14.07						14.				0.0348
												0.8										2.29														210
15.		1.18						16.				0.8						17.				2.29						18.					a.			210
b.	4,000 20													400 2								200				19.					a.			0.567909											b. 0.458
20.		61,400,000,000															21.			1.026 in.								22.							1.25 mi2
23.			0.004 in									24.				Saturday, $23.75														25.							0.42 g
26.			20.825 lb									27.				10.676							28.				a.	0.34									b.			0.416
29.		3.588						30.						56.86				31. 12										32.				41

																																30
33.			a.					–0.8							0.375
33.			a.					–0.8							0.375					0.6

							−1								0					1
b.
b.										–		9 –			5								2									16

				−5 − 4 −3 −2 −1 0 1 2 3 4 5
34.		$5.65						35.						37			36.			a. 1.08										b.		2.5625										37.		12, 12
38.			a.						b.							c.					d.					39.				11						40.						1
38.			a.						b.							c.					d.					39.				11						40.						30
																																										30
41.			a. 0.2										b.		1.3				c.	15				d. 11
	Chapters 1–4 Cumulative Review																																					(page 410)
	Chapters 1–4 Cumulative Review																																					(page 410)
1.		a. one hundred ﬁfty-four thousand, three hundred two
b.	100,000 50,000 4,000 300 2
2.	(3 4) 5														3 (4 5)											3.		16,693								4. 102
5.		75,625 ft2										6.			27 R 42							7. $715,600														8. 1, 2, 4, 5, 10, 20
9.	22 5 11											10.				600, 20						11.				4		12.											13.			13
14.			adding								15.				83°F increase											16.				270										17. 1
18.			2,100 ft											19. 3( 5)									15					20.						60
21.		8, 3, 36, 6, 6																22.		35			23.					5,000											24.				6
21.		8, 3, 36, 6, 6																22.		35			23.					5,000											24.			13
25.			equivalent fractions																			26.			5			27.				21								28.				3
25.			equivalent fractions																			26.						27.												28.				16
																							7							128														16
29.			17			30.					19			1		31. 26						7		32.							1					33.					7	34. 11				1	in.
29.		18				30.					19			8		31. 26						24		32.												33.				64		34. 11					in.
		18												8								24								3										64				8
35.		3				36.					0.001 in.							37.

		4

Appendix V		Answers to Selected Exercises			A-43
38.	9
1	– –
1	8
–3 –	–1.5	0.75		3.8
4	–1.5	0.75	4	3.8


		−5 − 4 −3 −2 −1 0 1 2 3 4 5
39.	130.198			40.	1.01	41.	8.136	42.	0.056012
43.	5.6		44.	0.0000897		45. 33.6 hr		46.	157.5 in.2
47.	232.8 48. 0.416					49.	2.325	50. 8, 8 51. 7
52.	15		53.	6	54. 39
52.	4		53.	6	54. 39

	Study Set Section 5.1																						(page 423)
1. ratio							3.	unit			5.			3				7.		10							9.		11 minutes													11

																													60 minutes													60
11.		13				, 13 to 9, 13 9									13.			5				15.						11				17.						5	19.				7			21.	2
11.				9		, 13 to 9, 13 9									13.				8			15.						16				17.						3	19.					4		21.	3
				9															8									16										3						4			3
23.		1				25.		1	27.				3		29.					1					31.				13						33.			19		35.					2

		2						3					4							3									3									39							7
37.		1				39.		6	41.				1		43.					3					45.				3			47.						7		49.					32 ft

		2						1					5							7									4									12							3 sec
51.				15 days				53.					21 made														55.					3 beats

					4 gal						25 attempts																			2 measures
57.				12 revolutions per min																	59. $5,000 per year
61.				1.5 errors per hr											63.				320.6 people per square mi
65.				$4 per min						67.				$68 per person																	69.						1.2 cents per ounce
71.				$0.07 per ft						73.				a.		2				b.						3		75.					1					77.			3
71.				$0.07 per ft						73.				a.		3				b.					2			75.				55						77.		1
79.				a. $1,800					b.		4				c.	1					d.						1		81.						1			83.		1

											9					3											18								1					20
85.				5 compressions										87.						329 complaints																			89.				a.		108,000

						2 breaths												100,000 passengers
b.		24 browsers per buyer																91.								7¢ per oz											93.		1.25¢ per min
95.				$4.45 per lb							97.				440 gal per min																	99.						a. 325 mi
b.		65 mph						101.			the 6-oz can																103.				the 50-tablet boxes
105. the truck									107. the second car																						113. 43,000											115. 8,000
	Study Set Section 5.2																						(page 438)
	Study Set Section 5.2																						(page 438)
1. proportion									3.			cross						5.				variable										7.					isolated						9.			true,
false						11. 9, 90, 45, 90									13.						Children, Teacher’s aides
15.		3 x, 18, 3, 3, 6, 6												17.				20									2		19.					400 sheets											4 sheets

																		30									3								100 beds										1 bed
21.				false			23.		true					25.				true									27.		false								29.		false
31.				true			33. true							35.			false										37.		yes							39. no						41.				6
43.		4				45.		0.3		47.				2.2				49.				3					1		51.					7				53.		3,500						55.	1
43.		4				45.		0.3		47.				2.2				49.				3					2		51.			8						53.		3,500						55.	2
																											2					8															2
57.		36					59.	1		61.			2		63.					8			1				65.				180						67.		18				69.			3.1
57.		36					59.	1		61.			2		63.					8		5					65.				180						67.		18				69.			3.1
71.		1				73.		$218.75						75.				$77.32										77.				yes						79.		24

		6
81.		975					83. 80 ft						85.			65.25 ft													65 ft 3 in.
										5										2																				1
87.			2.625 in.						2		in.				89. 4									, which is about 4																			91.			19 sec
87.			2.625 in.						2	8	in.				89. 4						7			, which is about 4																4			91.			19 sec
93.				31.25 in.					31		1		in.			95.				$309									101.						49.188					103.						31.428
93.				31.25 in.					31		4		in.			95.				$309									101.						49.188					103.						31.428
105. 4.1							107.		49.09

A-44												Appendix V														Answers to Selected Exercises
		Study Set Section 5.3																																	(page 452)
		Study Set Section 5.3																																	(page 452)
1.			length											3.		unit										5.			capacity											7.			a.	1				b.		3			c. 36
	d.			5,280									9. a.				8						b.				2			c.				1					d. 1				11.			1				13.					a. oz
	b. lb					15.								a.			1 ton												b.			2 pt								17.			a. iv						b. i						c. ii

																2,000 lb																1 qt
	d. iii					19.								a. iii							b. iv									c.			i					d. ii					21.			a. pound
	b. ounce													c. ﬂuid ounce																	23.								36, in., 72									25.				2,000, 16, oz,
32,000												27. a.					8					b.					5		in., 1					1			in., 2					7	in.			29.					a.		16

																											8								4							8
				9										3				3																				9												7
	b.					in., 1									in., 2										in.					31.				2							in.		33.					10				in.				35. 12 ft
	b.			16		in., 1								4	in., 2					16					in.					31.				2					16		in.		33.					10			8	in.				35. 12 ft
37.					105 ft									39.			42 in.												41.				63 in.									43.		21					mi			0.06 mi

																																													352
				7																											3																						1
45.						mi								0.875 mi													47.			2					lb						2.75 lb							49.				4		lb					4.5 lb
45.					8	mi								0.875 mi													47.			2			4		lb						2.75 lb							49.				4	2	lb					4.5 lb
51.					800 oz									53.				1,392 oz													55.								128 ﬂ oz							57.					336 ﬂ oz
						3												1																																					2
59.				2					hr					61.			5					hr							63.				6 pt								65. 5 days									67.					4			ft
59.				2			4		hr					61.			5		2			hr							63.				6 pt								65. 5 days									67.					4	3		ft
69.					48 in.									71.			2 gal										73.				5 lb							75.					4 hr					77.				288 in.
79.				2		1			yd						2.5 yd											81.				15 ft								83.				24,800 lb										85.			2		1		yd
79.				2			2		yd						2.5 yd											81.				15 ft								83.				24,800 lb										85.			2		3		yd
																																		1
87.					3 mi									89.		2,640 ft													91. 3										tons					3.5 tons									93.				2 pt
87.					3 mi									89.		2,640 ft													91. 3							2			tons					3.5 tons									93.				2 pt
95.					150 yd									97.				2,880 in.													99.								0.28 mi					101.							61,600 yd
103.						128 oz										105.							4			19			tons									4.95 tons								107.						68 quart cans
103.						128 oz										105.							4			20			tons									4.95 tons								107.						68 quart cans
						7
109.						71							gal				71.875 gal																111. 320 oz
109.						71				8			gal				71.875 gal																111. 320 oz
113.						6		1			days						6.125 days																	117.							a.		3,700						b.			3,670
113.						6					days						6.125 days																	117.							a.		3,700						b.			3,670
						8
	c.	3,673.26													d.		3,673.3
		Study Set Section 5.4																																	(page 466)
		Study Set Section 5.4																																	(page 466)
1.			metric											3. a. tens b. hundreds c. thousands																																									5. unit,
	chart								7. weight														9.					a.		1,000									b.			100			c.			1,000
11.					a. 1,000											b.		10									13.			a.							1 km							b.			100 cg

																																			1,000 m														1 g
	c.		1,000 milliliters																				15.						a. iii										b. i				c. ii					17.				a. ii							b. iii

									1 liter
									1 liter
	c. i					19.						1, 100, 0.2														21.				1,000, 1, mg, 200,000																						23. 1 cm,
	3 cm, 5 cm													25.				a. 10, 1 millimeter																									b.		27 mm, 41 mm,
	55 mm											27. 156 mm															29.					280 mm											31.			3.8 m							33.				1.2 m
35.					8,700 mm												37.							2,890 mm														39.				0.000045 km
41.					0.000003 km													43.										1,930 g										45.				4,531 g								47.			6 g
49.					3.5 g									51.			3,000 mL													53. 26,300 mL																		55.				3.1 cm
57.					0.5 L									59.			2,000 g												61.					0.74 mm										63.					1,000,000 g
65.					0.65823 kL													67.								0.472 dm												69.					10	71.						0.5 g
73.					5.689 kg											75. 4.532 m																		77. 0.0325 L														79.				675,000
81.				0.0000077													83.								1.34 hm									85.							6,578 dam											87.			0.5 km,
	1 km, 1.5 km, 5 km, 10 km																														89.								3.43 hm							91.					12 cm, 8 cm
93.					0.00005 L												95.							3 g						97.					3,000 mL									99. 4									101.					3 mL

107.						0.8						109.					0.07
		Think It Through																											(page 473)
		Think It Through																											(page 473)
1.			216 mm 279 mm																										2. 9 kilograms															3.					22.2 milliliters

Study Set Section 5.5

(page 476)

1. Fahrenheit, Celsius

a. meter

b. meter

c. inch

d. mile

a. liter b. liter

c. gallon

7. a.

0.03 m

1 ft

0.45 kg

3.79 L

9. 0.30 m, m

11.

0.035, 1,000, oz

1 lb

1 gal

13.

10 in.

15.

34 in.

17.

2,520 m

19.

7,534.5 m

21.

9,072 g

23. 34,020 g

25. 14.3 lb

27. 660 lb

29.

0.7 qt

31.

1.3 qt

33.

48.9°C

35. 1.7°C

37.

167°F

39.

50°F

41. 11,340 g

43.

122°F

45.

712.5 mL

47.

17.6 oz

49. 147.6 in.

51. 0.1 L

53. 39,283 ft

55.

1.0 kg

57.

14°F

59.

0.6 oz

61.

243.4 ﬂ oz

63.

91.4 cm

65. 0.5 qt

67.

10°C

69.

127 m

71.

20.6°C

73.

5 mi

75. about 70 mph

77.

1.9 km

79.

1.9 cm

81.	411 lb, 770 lb	83. a. 226.8 g					b. 0.24 L	85. no
87.	about 62°C	89.	28°C		91.	5°C and 0°C
93.	the 3 quarts	99.		29	101.	4	103. 8.05	105. 15.6
			15			5

	Chapter 5 Review							(page 479)
1.		7	2.	15	3.	2	4.		3	5.		1	6.	7	7.	4	8.	3
	25			16		3		2			3			8		5		1
9.	7		10.	5	11.	1	12.			1	13.		16 cm		14.		$3

	8			4		12				4			3 yr				5 min

15.		30 tickets per min																			16.							15 inches per turn
17.		32.5 feet per roll																		18. 3.2 calories per piece
19.		$2.29 per pair												20.							$0.25 billion per month
21.		37					22.				$7.75								23.			1,125 people per min
21.	32						22.				$7.75								23.			1,125 people per min
24.		the 8-oz can												25. a.										20					2			b.			6 buses										36 buses

																								30					3					100 cars											600 cars
26.	2, 54, 6, 54											27.							false					28.					true				29.				true							30. true
31.		false						32.					false						33.						yes				34.			no				35. 4.5									36.		16
37.	7.2							38.			0.12			39.							1			1				40.		3	1		41.					1				42.			1,000
37.	7.2							38.			0.12			39.							1			2				40.		3	2		41.				3					42.			1,000
43.		192.5 mi										44.		300							45.							12 ft				46.				30 in.							47. a.				16
b.	7		in., 1						1	in., 1				3			in., 2					5			in.				48.			1	1		in.				49.						1 mi			1,
b.	16		in., 1							in., 1				4			in., 2								in.				48.			1	2		in.				49.					5,280 ft				1,
	16							2						4							8												2											5,280 ft
5,280 ft								1				50.		a. min													b. sec					51.				15 ft							52. 216 in.

1 mi
1 mi
	1																				3
53.	5				ft				5.5 ft							54. 1											mi		1.75 mi								55.					54 in.
53.	5			2	ft				5.5 ft							54. 1							4				mi		1.75 mi								55.					54 in.
56.		1,760 yd										57.			2 lb						58.							275.2 oz					59.						96,000 oz
	1																																						1
60.	2				tons							2.25 tons												61. 80 ﬂ oz									62.								gal					0.5 gal
60.	2			4	tons							2.25 tons												61. 80 ﬂ oz									62.							2	gal					0.5 gal
63.		68 c						64.				5.5 qt							65.							40 pt				66.			56 c						67.					1,200 sec
														1
68.		15 min									69. 8							days						70.					360 min								71.					108 hr
68.		15 min									69. 8				3			days						70.					360 min								71.					108 hr
72.	86,400 sec											73.		21						mi 0.12 mi												74.				20			1		tons					20.25 tons
72.	86,400 sec											73.				176				mi 0.12 mi												74.				20			4		tons					20.25 tons
75.	484						2	yd				76.		100							77.							a. 10, 1 millimeter
75.	484						3	yd				76.		100							77.							a. 10, 1 millimeter
							3
b. 19 mm, 3 cm, 45 mm, 62 mm																														78.			4 cm
79.		a.					1 km							1,					1,000 m										1			b.				1 g								1,		100 cg		1

						1,000 m													1 km															100 cg												1 g
80.		5 places to the left																			81.							4.75 m					82.				8,000 mm

83.	165,700 m	84. 678.9 dm		85. 0.05 kg		86.	8 g
87.	5.425 kg	88. 5,425,000 mg		89.	1.5 L	90.	3.25 kL
91.	40 cL 92. 1,000 dL		93. 1.35 kg		94.	0.24 L 95. 50
96.	1,000 mL	97. 164 ft	98.	Sears Tower		99.	3,107 km

100.	198 cm 101. 850.5 g 102.		33 lb	103. 22,680 g
104.	about 909 kg	105. about 2.0 lb		106. LaCroix
107.	about 159.2 L	108. 221°F	109. 25°C 110. 30°C

	Chapter 5 Test								(page 494)
1. a. ratio						b. rate				c. proportion										d. cross						e. tenths,
hundredths, thousandths												f.	metric							g.			Fahrenheit,
Celsius						9	, 9 13, 9 to 13 3.											3				1			2		6
				2.															4.					5.			6.
					13													4				6			5			7
7.			3 feet			8.		the 2-pound can											9.		22.5 kwh per day

		2 seconds
10.			15 billboards						3 billboards									11.			a. no				b. yes
			50 miles							10 miles

12.			yes	13.		15		14.		63.24			15.					2	1		16.			0.2			17. $3.43

																			2
			2 c				16			5		in., 1			3		in., 2				3		in.				introduce,
18.				19.		a.			b.															20.
											16				8						4
eliminate					21.		15 ft			22.		8	1	yd				23.			172 oz					24. 3,200 lb
													3

25.			128 ﬂ oz			26.		115,200 min								27. a. the one on the left
b. the longer one								c. the right side												28. 12 mm, 5 cm,
65 mm				29.		0.5 km				30.		500 cm						31.				0.08 kg
32.			70,000 mL				33.		7.5 g			34.			the 100-yd race												35. Jim
36.			0.9 qt		37.		42 cm			38.			182°F						39.				A scale is a ratio

(or rate) comparing the size of a drawing and the size of an actual object. For example, 1 inch to 6 feet (1 in. 6 ft).

40. It is easier to convert from one unit to another in the metric system because it is based on the number 10.

	Chapters 1–5 Cumulative Review																							(page 496)
1.	a. ﬁve million, seven hundred sixty-four thousand,
ﬁve hundred two
b.	5,000,000 700,000 60,000 4,000 500 2
2.	a. 186 to 184								b. Detroit						c.				370 points							3.			69,658
4.	367,416					5. 20 R3					6.		$560						7. 1, 2, 3, 5, 6, 10, 15, 30
8.	23 32 5					9.			140, 4			10. 81							11.				12.			4
13.		15 shots				14. 9, 9							15.		a. 8							b. undeﬁned									c. 8
d.	0		e. 8			f. 0			16.		30		17.		5,000								18.			4			19.		54

																												5			60
		59,100,000 sq mi												A	1				bh		22. 1								9
20.											21.															23.
20.											21.							2								23.				20
		19				31							9						3										26			11
24.				25.				in. 26.				6				27.					hp		28.								1
24.		15		25.			32	in. 26.				6		10		27.				4	hp		28.						15		1	15
29.				30.															11		3
													3						––		= 1–
													3						8		8
													–1–
										–3.2			4		–0.5						2.25				9

							−5 − 4 −3 −2 −1 0 1 2 3 4 5
31.		17.64				32.			23.38				33.		250						34.		458.15 lb
35.		0.025			36. 12.7						37.		0.083						38.		$9.95				39.				23
40.		1		41.	the 94-pound bag												42. false						43.				202 mg
40.		5		41.	the 94-pound bag												42. false						43.				202 mg

										Appendix V Answers to Selected Exercises																																									A-45
44.		15					45.		a.					960 hr								b.		4,320 min												c.			480 sec
46.		2.5 lb							47.					2,400 mm											48. 0.32 kg
49.		a.			1 gal						b. a meterstick															50.							36 in.
	Study Set Section 6.1																								(page 509)
	Study Set Section 6.1																								(page 509)
1.	Percent								3.					100, simplify												5.						right			7.							percent
9.	84%, 16%												11.				107%								13. 99%										15.							a.			15%				b.	85%
17.		17						19.					91				21.				1				23.						3			25.							19						27.		547

		100									100										25										5							1,000											1,000
		1							17									1								17												13									11
29.				31.												33.							35.											37.											39.
29.		8		31.					250							33.		75					35.			120								37.				10							39.			5
41.			7						43.					1				45.					0.16								47.			0.81							49.					0.3412

		2,000												400
51.		0.50033									53.					0.0699							55.			0.013								57.							0.0725							59.		0.185
61.		4.6					63.				3.16						65.				0.005					67.							0.0003								69.						36.2%
71.		98%						73.					171%								75.				400%								77.		40%										79.			16%
81.		62.5%							83.					43.75%									85.			225%									87.						105%
				2		% 16.7%																				2							166.7%
89.		16																91.					166							%
89.		16		3														91.					166					3		%
93.		157						, 3.14%									95.					51			, 0.408								97.					21					, 0.0525
93.		5,000						, 3.14%									95.				125				, 0.408								97.				400						, 0.0525
									1			% 233.3%
99.		2.33, 233																								101.							91%								103.						a.	12%
99.		2.33, 233								3																101.							91%								103.						a.	12%
b.	24%							c.	4% (Alaska, Hawaii)																								105.						a. 0.0775										b.	0.05
c.	0.1425							107.							torso: 27.5%											109.								a.	5									b.			0.078125

																																			64
																		1					1																	13
c.	7.8125%										111.						33	1		%,			1		, 0.3						113.				a.					13
c.	7.8125%										111.						33	3		%,			3		, 0.3						113.				a.			15
b.	86		2		%			86.7%										115.					a.			1			%				b.		1										c.		0.0025

			3																							4									400
117.			0.27%								123.						a.		34 cm								b.				68.25 cm2
	Think It Through																					(page 529)
	Think It Through																					(page 529)

36% are enrolled in college full time, 43% of the students work less than 20 hours per week, 10% never

	Study Set Section 6.2																(page 529)
1.	sentence, equation													3.	solved						5.	part, whole					7.			cross
9.	Amount, base, percent, whole																				11.	100%			13. a.					0.12
b.	0.056			c.	1.25					d.			0.0025
15.		a. x		7% 16,							x					7			b.		125		x 800,					125					x
															100												800					100
									16
c.	1	94% x,						1				94			17.			a.		5.4% 99					x,			x			5.4
								x	100																					100
																									99
									15					75.1													3.8						x
b.	75.1% x						15,												c. x 33.8					3.8,
										x				100												33.8						100
19.		68	21.		132				23.				17.696					25.			24.36		27.		25%
29.		85%		31.		62.5%								33.		43.75%						35.	110%				37.			350%
39.		30	41.		150				43.				57.6			45.				72.6		47.		1.25%					49.			65
51.		99	53.		90		55.						80%			57.			0.096			59.		44	61.				2,500%
63.		107.1		65.			60		67.					31.25%						69.		43.5
71.		12K bytes						12,000 bytes											73.		a. $20.75				b. $4.15
75.		2.7 in.			77.			yes					79.		5%				81. 120				83. 13,500 km
85.		$1,026 billion							87.					24 oz				89.			30, 12			91.	40,000%

A-46	Appendix V	Answers to Selected Exercises
93.	Petroleum 14%	Renewable 10%
		Nuclear
		12%
	Natural gas
	32%	Coal 32%

95. 32%, 43%, 13%, 6%, 6%;					2007 Federal Income Sources
			Social Security,
				Medicare,
			unemployment
				taxes		Personal
				32%		Personal
						income
						taxes
						43%
			Borrowing 6%
				Excise, estate,
				customs taxes		Corporate
					6%	income taxes
						13%
103.	18.17	105.	5.001	107.	0.008
Think It Through				(page 543)

1.1970–1975, about a 75% increase

2.2000–2005, about a 15% decrease

	Study Set Section 6.3															(page 546)
1. commission										3.		a. increase					b. original									5.	purchase
price			7.		sales					9.		a. $64.07					b. $135.00								11.		subtract,
original					13.				$3.71				15.		$4.20		17.					$70.83				19.		$64.03
21.		5.2%			23. 15.3%									25.		$11.40					27.			$168			29.		2%
31.		4%			33.				10%			35.		15%			37.			20%					39.	10%
41.		$29.70, $60.30										43.		$8.70, $49.30									45.		19%			47. 14%
49.		$53.55					51.			$47.34, $2.84, $50.18													53.		8%		55.		0.25%
57.		$150			59.				8%, 3.75%, 1.2%, 6.2%															61. 5%				63. 31%
65.		152%					67.			36%			69. 12.5%							71.			a.		25%		b.		36%
73.		$2,955					75.			1.5%				77.		90%			79.				$12,000
81.		a. $7.99							b. $31.96						83. 6%					85.			$349.97, 13%
87.		23%, $11.88									89.		$76.50				91.		$187.49						97.		50
99.		3	101.				13
	Study Set Section 6.4															(page 557)

1. Estimation										3.	two			5.		2	7.		4			9.		10, 5		11. 2.751, 3
13.		0.1267, 0.1								15. 405.9 lb, 400 lb												17.		69.14 min, 70 min
19.		70		21.			14			23.			2,100,000				25.				200,000					27.		4	29.	12
31.		820			33.				20		35.		$9		37.		$4.50						39.		$18		41.		$1.50
43.		8	45.			72				47.		12		49.		5.4			51.			180			53.		230		55.	6
57.		18		59.			7			61.		70		63.		12,000						65.		1.8		67.		0.49
69.		12		71.				164 students							73.		$60					75.		$6		77.		$7.50
79.		$30,000					81.				320 lb				83. 210 motorists											85.		220 people
87.		18,000 people										89.		3,100 volunteers
			4				1					1			5		5						2
95.		a.			1					b.			c.			d.						1
			3					3				3			12			3					3

	Study Set Section 6.5																														(page 566)
1.		interest									3.						rate					5. total												7.		a. $125,000												b.					5%
c.		30 years											9.				a.	0.07							b.			0.098										c.			0.0625						11.						$1,800
13.				a. compound interest																								b. $1,000														c.			4		d. $50
e.		1 year									15.						I		Prt						17.				$100									19.				$252
21.			$525								23.					$1,590							25.					$16.50										27. $30.80
29.			$13,159.23													31.				$40,493.15														33.						$2,060.68
35.			$5,619.27													37.				$10,011.96														39.				$77,775.64										41.							$5,300
43.			$198								45.					$5,580							47.					$46.88										49. $4,262.14
51.			$10,000, 7											1		%				0.0725, 2 yr, $1,450																						53. $192, $1,392, $58

														4
55.				$19.449 million																57.					$755.83											59.						$1,271.22
61.			$570.65											63.				$30,915.66											65.							$159,569.75
			1								29											1
71.					73.											75.				8					77.				36
71.			2		73.						35					75.				8		3			77.				36
	Chapter 6 Review																								(page 570)
	Chapter 6 Review																								(page 570)
1.	39%, 0.39,													39				2.				111%, 1.11,														111						3. 61%								4.					a.	54%
1.	39%, 0.39,													100				2.				111%, 1.11,														100						3. 61%								4.					a.	54%
b.			46%						5.				3				6.				6		7.				37							8.					1						9.	0.27							10.			0.08
b.			46%						5.				20				6.			5			7.			400								8.				500							9.	0.27							10.			0.08
11.			6.55						12.					0.018								13.				0.0075										14.					0.0023						15.						83%
16.			162.5%											17.				5.1%							18.				600%											19.					50%			20.						80%
																													1			% 33.3%																1			% 83.3%
21.			87.5%								22. 6.25%												23. 33																						24. 83
21.			87.5%								22. 6.25%												23. 33							3															24. 83				3
					2			% 91.7%																					2				% 166.7%
25.			91																			26.			166																						27.			a.				0.972
25.			91		3																	26.			166						3																27.			a.				0.972
b.			243						28.				63%							29.				a.		0.0025											b.					1			30.			6		2		% 6.7%

			250																																					400										3
31.				a. amount: 15, base: 45 percent: 33																																					1		% b.				Amount, base,
31.				a. amount: 15, base: 45 percent: 33																																					3		% b.				Amount, base,
percent									32.					a. 0.13									b.			0.071									c.			1.95							d.		0.0025
e.			1		f.				2			g.				1		33.					a. x						32% 96															b.		64				x 135

			3						3							6
c.	9					47.2% x												34.					a.			x								32						b.				64				x
c.	9					47.2% x												34.					a.		96									100						b.		135					100
	9				47.2													200										125												1.75%										2,100
c.														35.									36.											37.													38.
c.		x			100									35.									36.											37.													38.
39.			121						40.					30				41.				600						42.						5,300%								43.					0.6 gal methane
44.			68						45.				87%							46.			$5.43																			139,531,200 mi2
47.										Family/friends																										48.						139,531,200 mi2
				Other 5%										5%																						49.						$3.30, $63.29
				Other 5%																																50.						4%				51. $40.20
																																				50.						4%				51. $40.20
																																				52.						4.25%						53.					$100,000
							Internet																													54.						original								55.					18%
							Internet																													56.						9.6%
									15%													College														57.						a. purchase price
																																				57.						a. purchase price
																																					b. sales tax
						Local bank																	57%														b. sales tax
						Local bank																															c.			commission rate
									18%																												c.			commission rate
																																				58.						a. sale price
																																					b. original price
																																					c.			discount
																																					c.			discount
59.			$180, $2,500, 7.2%																				60.						5%							61.					3.4203, 3
62.			86.87, 90												63. 4.34 sec, 4 sec																					64.					1,090 L, 1,000 L
65.			12						66.				120					67.					140,000											68.				150							69.		3			70.					10
71.			350						72.					1,000						73.					60				74. 2											75.					$36		76.						$7.50
77.				about 12 ﬂuid oz																			78.				about 120 people																				79. 200

80.	$30,000	81. $6,000, 8%, 2 years, $960			82.	$27,240
83.	$75.63	84.	$10,308.22	85. a. $116.25 b.		1,616.25
c. $134.69		86.	$2,142.45	87. $6,076.45	88. $43,265.78

	Chapter 6 Test																	(page 588)
1.	a. Percent											b. is, of, what, what																	c. amount, base
d. increase										e. Simple, Compound																			2.		a. 61%,								61						, 0.61
																																							100
b.		39%						3.		199%,						199				, 1.99						4.	a.	0.67				b.			0.123
																100
c.	0.0975								5.			0.0006							b.		2.1					c.	0.55375					6.			a.				25%
b.		62.5%							c.			112%							7.		a.		19%				b.		347%						c.		0.5%
8.	a.		66.7%									b.		200%							c.		90%
9.	a.			11					b.				1						c.		5		10.				a.	1			b.		3			c.					2
			20							10,000											4							15					8						25
					1																		7
11.		a.			3			%				3.3%							b.		177				%			177.8%							12.				6.5%
						3																		9
13.		250%							14.				93.7%								15.		90				16.		21			17.			134.4							18.					7.8
19.		a.			1.02 in.								b.		32.98 in.								20.				$26.24					21.			3%							22.				23%
23.		$35.92								24.				11%					25.				$41,440						26. $9, $66, 12%
27.		$6.60, $13.40													28.				a. two, left									b. one, left											29. a.							80
b.	3,000,000											c.		40		30.					100					31. $4.50						32. 16,000 females
33.		$150							34.			$28,175									35.		$39.45						36.			$5,079.60
	Chapters 1–6 Cumulative Review																															(page 591)

1.	a. six million, ﬁfty-four thousand, three hundred forty-six
b.		6,000,000 50,000 4,000 300 40 6																																			2. 239
3.	42,156								4.			23,100							5.		15 R6						6.		80 servings										7. 1, 2, 4,
5, 8, 10, 20, 40												8.			2 3 72								9.			120, 6				10. 15							11.									12. 0
13.		$135								14.				36, 36							15.					a. undeﬁned									b.				0					c. 0
d.		14			16.				30						17.				1,900							18.		9			19.		36						20. 60

																												10					45
21.		650 in.2								22.						3			23.				24			24.			7		25.		1				lb					26.				30

																	4						35						6					12
27.		35			3		in.			28.						5			29.			a.				452.03				b.		452.030										30.				5.5
					4											6
																																								5
31.		$731.40								32.				0.27					33.				0.73				34.			29			35.									36.					4
																																							6
37.		40 days								38.				2.4 m							39. 14.3 lb									40.		29%,							29				, 0.473,
																																						100
473			, 87.5%, 0.875													41.					125					42. 0.0018%									43. 78%
1,000

44.		$428, $321, $107, 25%																				45.				a. $12				b. $90.18									46. $1,450
	Study Set Section 7.1																							(page 602)

1.	(a)				3.				(c)				5.		(d)				7.			axis					9.	intersection
11.		pictures										13.			bars, edge, equal														15.		about 500 buses
17.		$10.70								19.				$4.55 ($21.85 $17.30)																		21.			ﬁsh, cat, dog
23.		no			25.					yes					27.				about 10,000,000 metric tons
29.		1990, 2000, 2007																	31. 4,000,000 metric tons																					33. seniors
35.		$50						37.			Chinese								39.				no				41.		62%				43.				1,219,000,000
45.		493						47. 2002 to 2003; 2004 to 2005; 2005 to 2006;
2007 to 2008												49.			2001 and 2003												51.			2005 to 2006;
a decrease of 14 resorts																					53.		1			55.		B		57.			1				59.					Runner 1
was running; runner 2 was stopped.																													61.		a.		27						b.			22
63.		$16,168.25											65.					a. $9,593.75									b. $6,847.50												c. $2,746.25
67.		2000; about 3.2%																	69.			increase; about 1%																	71. it
increased									73.				D					75. reckless driving and failure to yield

Appendix V	Answers to Selected Exercises			A-47
77. reckless driving 79.	about $440 81.	no	83.	the
miner’s 85. the miners	87. about $42	89.	about $30

91. 11% 93. 21%

95.Number of U.S. Farms

	6.0
	5.0
Millions	4.0
	3.0

	2.0
	1.0
	1950	1960	1970	1980	1990	2000	2007

Source: U.S. Dept. of Agriculture

97. $600

	item	$500
		$400
	of the
		$300
	price
		$200
	Sale

		$100

$100 $200 $300 $400 $500 $600 Original price of an item

101. 11, 13, 17, 19, 23, 29 103. 0, 4

Think It Through (page 616)

Median Annual Earnings of Full-Time Workers (25 years and older) by Education

	$70,000	$64,028
		$64,028
	$60,000
	$50,000	$50,993
	$50,000
	$40,000	$38,375
	$40,000	$33,630
		$33,630
	$30,000	$30,815
	$30,000
		$22,212
	$20,000
	$10,000
	$0

Less than a		High	Some		Associate Bachelor’s Master’s
high school	school		college		degree		degree		degree
diploma	graduate
$8,603		$2,815		$4,745		$12,618		$13,035
more		more		more		more			more

Source: Bureau of Labor Statistics, Current Population Survey (2008)

	Study Set Section 7.2							(page 617)
1. mean			3.	mode		5.	the number of values					7.	a. an even
number			b.	6 and 8		c. 6, 8, 14, 7			9.	8	11.	35	13.	19
15.		5.8	17.	9	19.	5	21.	17.2	23.	5	25.	9	27.	44
										8
29.		2.05	31.	1	33.	3	35.	6	37. 22.7		39. bimodal:				1	,	1
																	2
														3


A-48				Appendix V				Answers to Selected Exercises
41.			a.	82.5	b.	83	43. a. 2,670 mi				b.	89 mi
45.			a.	$11,875		b.	125		c. $95	47.	a. 65¢		b. 60¢
	c. 50¢			49.	61°	51.		2.23 GPA		53.	2.5 GPA 55. median
	and mode are 85 57. same average (56); sister’s scores are
	more consistent					59.		22.525 oz, 25 oz			61. 6.8, 6.9
63.			5 lb, 4 lb		69.		65%		71. 42	73.	62.5%		75.	43.5
		Chapter 7 Review							(page 621)

1.		a. 18°			b. 71°				2. a. 30 mph		b.	15 mph		3. 20
4.		about 59			5.	Germany and India; about 17							6.	about 35
7.		about 29%				8.	men; about 15% more					9.	women

10.No, I would not date a co-worker (31% to 29%)

11.about 4,100 animals 12. the Columbus Zoo; about

7,250 animals			13.	about 3,000 animals			14. about
12,500 animals			15.	oxygen	16.	4%	17. 13.5 lb
18.	166 lb	19.	about 3,000 million eggs 20. about
3,050 million eggs 21. 2007; about 2,950 million eggs
22.	about 5,750 million eggs				23.	between 2006 and 2007
24.	between 2007 and 2008				25.	about 290 million more
eggs 26.		about 500 million more eggs					27. 60 28. 180

29.160

30.110

		90
	Frequency	70
	Frequency	50
		50
		30
		10

			3.0	8.0	13.0	18.0	23.0
		Hours of TV watched by the household
31.	yes	32.	median	33. 1.2 oz			34. 1.138 oz
35.	7.3 microns, 7.2 microns, 6.9 microns 36. 32 pages
per day		37.	$20 38. 2.62 GPA


	Chapter 7 Test			(page 630)
1.	a. axis	b. mean		c. median		d. mode			e. central
2.	a. 563 calories		b. 129 calories				c. about 8 mph
3.	a. love seat; 130 ft			b.	50 feet more			c. 340 ft		4. a. 75%
b.	14.1%	c. lung cancer			d. prostate cancer; 32.7%
5.	a. about 38 g		b. about 15 g			6.	a.	17%	b.	529,550
7.	a. about 27,000 police ofﬁcers					b. 1989; about 26,000
police ofﬁcers c. 2000; about 41,000 police ofﬁcers
d. about 5,000 police ofﬁcers 8.						a. bicyclist 1

b. Bicyclist 1 is stopped, but is ahead in the race. Bicyclist 2 is

beginning to catch up.			c. time C		d.	Bicyclist 2 never lead.
e. bicyclist 1	9.	a. 22 employees			b.	30 employees
c. 57 employees		10.	a. 7.5 hr	b.	7.5 hr c. 5 hr
11. 3 stars	12.	3.36 GPA 13.		mean: 4.41 million; median:
4.25 million; mode: 4.25 million				14. Of all the existing

single-family homes sold in May of 2009, half of them sold for less than $172,900 and half sold for more than $172,900.

Chapters 1–7 Cumulative Review (page 633)

1. Fifty-two million, nine hundred forty thousand,

ﬁve hundred ﬁfty-nine; 50,000,000 2,000,000 900,000

40,000 500 50 9																2.	50,000						3.	54,604				4. 4,209
5.	23,115							6.		87				7.	683 459							1,142				8.	10,912 in.2
9.	2011						10.				a. 1, 2, 3, 6, 9, 18										b.	2 32				11. 2, 3, 5, 7, 11,
13, 17, 19, 23, 29												12.			a.	24			b.		4	13. 35					14.			9
15.

			−4					−3 −2						−1		0			1			2		3		4
			−4					−3 −2						−1		0			1			2		3		4
16.		a.		6				b.		5			c.	false		17.				a. 20					b.	30			c. 125
d.	5			18.				1,100°F						19.		5			20. 429					21. 4						22. 200
				5						3			24. a. 0				b. undeﬁned											8			4
23.		a.						b.																		25.					26.
23.		a.		9				b.		2																25.		35			26.	9
				1						19					160 min									21			1			1
27.							28.							29.							30.
27.				6			28.			20				29.							30.				20					20
		3												5			3
31.		6				in.		32.				10			33.						34.		428.91				35.			$1,815.19
31.		6	4			in.		32.				10		8	33.			8			34.		428.91				35.			$1,815.19
36.		a.		345					b.			0.000345					37. 145.5						38. 0.744								39. 745
																							2								1
40.		0.01825								41. 0.72						42. 75					43.			44.			$59.95				45.
40.		0.01825								41. 0.72						42. 75					43.		3	44.			$59.95				45.		7
46.		128 ﬂ oz								47.				6.4 m		48.				19.8°C				49.			3		, 0.03, 2.25,

																										100
225%,					41				, 4.1% 50.							17%					51.		24.36			52.		57.6
225%,				1,000					, 4.1% 50.							17%					51.		24.36			52.		57.6
				1,000
53.		$7.92						54.				16%			55.		$12				56.		$3,312				57.			$13,159.23
58.		a.		7%					b.			5,040			59.		a. 2008; 36								b.	2007 to 2008;
an increase of 16 deaths c. 2008 to 2009; a decrease of
8 deaths								60. mean: 3.02; median: 3.00; mode: 2.75

	Study Set Section 8.1													(page 644)
1.	Variables						3. expressions							5.		terms				7.		coefﬁcient
9.	(12 h) in.							11.		a. (x 20) ounces b.												(100 p) lb
13.		5, 25, 45				15.			4x	17.		2w			19. a. x y									y x
b. (r s) t								r (s t)						21.	0 s				0 and s 0							0
23.		a.	4	b. 3, 11, 1, 9								25. 6, 75, 1,							1, 1, 1					27.		term
		factor						l 15					50x				w		2	5			P		2p
29.					31.						33.					35.				37.
		k2 2,005								2a 1						1,000		l							3
39.								41.						43.					45.			2p 90
		3(35 h 300)														n				4d 15
47.										49.		p 680					51.
53.		2(200 t)						55.		0a 2			0	57. 0.1d or							1	d

59.		three-fourths of r									61.		50 less than t							10

63.		the product of x, y, and z												65. twice m, increased by 5
67.		(x 2) in.						69.		(36 x) in.						71. 2				73.			13			75. 20
77.		12		79.		5			81.		1			83.		17	85.			36			87.			255
												5
89.		8	91.		a. Let x						weight of the Element (in pounds);
2x 340 weight of the Hummer (in pounds)																								b. 6,400 lb
93.		a. let x					age of Apple; x 80											age of IBM;
x 9				age of Dell						b. IBM: 112 years; Dell: 23 years
99.		60		101.			8
						27

	Study Set Section 8.2													(page 655)

1.	simplify				3.			distributive						5.	like			7.		a. 4, 9, 36
b. associative property of multiplication																				9. a.						b.
c.			d.			11.			a.	10x		b. can’t be simpliﬁed													c. 42x
d. can’t be simpliﬁed											e.	18x			f.	3x 5				13.				a. 6(h 4)
b. (z 16)								15. 12t			17.			63m		19.			35q					21.		300t
23.		11.2x			25.			60c		27. 96m						29.	g			31.			5x		33. 6y

35.	5x 15		37.	12x 27				39.	9x 10			41.	0.4x 1.6
43.	36c 42 45. 78c 18							47. 30t 90				49. 4a 1
51.	24t 16		53.	2w 4			55.	56y 32
57.	50a 75b 25				59.		x 7		61. 5.6y 7
63.	3x, 2x 65.			3m3, m3				67.	10x		69.	0
71.	20b2 73. r			75.	28y		77.	s3		79.	3.6c		81. 0.4r
83.	4 t 85. 5 x			87.	6y 10				89.	2x 5
	5		8				4x2 3x 9				95. 7z 15
91.	does not simplify				93.
97.	s2 12		99.	41r 130				101. 8x 9				103. 12c 34
105.		10r	107.	20r		109. 3a			111. 9r 16
113.		6x 115. c 13				117. a3 8				119.		12x
121.		(4x 8) ft		125. 2

	Study Set Section 8.3															(page 666)
1.	equation					3.		solve				5. equivalent										7.			a. x 6
b. neither					c. no				d.		yes				9. a. c, c						b. c, c
11.		a. x		b. y				c. t			d. h					13. 5, 5, 50, 50, , 45, 50
15.		a. is possibly equal to													b. yes				17.				no			19.			no
21.		no		23.		no		25.			yes				27.		no		29.				no			31.			yes				8
33.		yes		35.		yes 37.						71			39.		18		41.			0.9						43.		3		45.
47.		3	49.				1	51.		2.3						53.		45	55.					0		57.			21				9

		2.64				25		20					15					6								4 69. 4							7
59.					61.					63.						65.					67.											71.
73.		1	75.		6			77.		20			79.			0.5		81. 18								83.					4

85.		13		87.	2.5			89.			8		91.				13	93.			4			95.				5		21

		200						95				3	65°				20		$6,000,000													0
97.					99.				101.								103.												109.
111.			45 x
	Study Set Section 8.4															(page 673)

1.	solve			3.		simplify						5.	4, 9				7. subtraction, multiplication
9.	a. 2x 8							24				b. 20						3x 16								11.		a. no
b. yes				13. 7, 7, 2, 2, 14,									, 28, 21, 14									15.				6		17.		5
19.		7		21.		0.25			23.					5		25.		3			27.					10		29.		6
																										3
													2
31.		18		33.	16			35.		2.9			37.				4		39.				11			41.			41
																						5
43.		6		45.		0.04			47.			6				49.		11				51.				7		53.		11
55.		1	57.		9	59.			4			61.				3	63.			1		65.					5	67.		45
					2														4							6
69.		49		71. 1				73.			12					75. 6			77.					5				79.		3.5
83.		commutative property of multiplication
85.		associative property of addition
	Study Set Section 8.5															(page 683)

1. Analyze, equation, Solve, conclusion, Check																													3.	division
5.	addition					7.		borrow, add								9. equal-size discussion groups,
division				11.			s 6			13.			g 100					15.			1,700, 425, jar, age,
addition, 1,700, x, 1,700, 425, 425, 1,275, 1,275, 1,275, 1,700
17.		88, 10, ﬁrst class, economy, ﬁrst class, 10, 10x, 10x, 88, 11x,
11, 11, 8, 8, 80, 10, 80, 88												19.			She will need to borrow $248,000.
21.		Alicia could read 133 words per minute before taking the

course. 23. It will take 17 months for him to reach his goal. 25. Last year 7 scholarships were awarded. This year 13 scholarships were awarded. 27. She has made 6 payments. 29. 50 cent earned $150 million in 2008. 31. The length of the room is 20 feet and the width is 10 feet. 33. The scale would register 55 pounds. 35. The ﬁrst act has 5 scenes.

							Appendix V Answers to Selected Exercises																									A-49
37.				The value of the beneﬁt package is $7,000.
39.				His score for the ﬁrst game was 1,568 points.
41.				There were 6 minutes of commercials and 24 minutes of
the program. 43. They spend 150 minutes in lecture and
100 minutes in lab each week. 45. The shelter received
32 calls each day after being featured on the news.
47.				Three days ago, he waited for 35 minutes.
49.				The initial cost estimate was $54 million.
51.				The monthly rent for the apartment was $975.
53.				She must complete 4 more sessions to get the certiﬁcate.
61.			600, 20				63.			140, 14						65.				3,528; 1						67.		2,178; 22
	Study Set Section 8.6																			(page 694)

1.		exponential							3.			3x, 3x, 3x, 3x, ( 5y)3															5. a. add
b. multiply							c.		multiply									7.		a.	2x2			b. x4				9. a. doesn’t
simplify					b. x5					11.				x6, 18					13.			base 4, exponent 3
15.				base x, exponent 5												17.			base 3x, exponent 2
19.				base y, exponent 6												21.			base m, exponent 12
23.				base y 9, exponent 4															25.			m5		27.			(4t)4			29. 4t5
31.				a2b3	33.			57				35. a6						37.			b6		39.			c13		41.		a5b6
43.				c2d5	45. x3y11									47. m200							49.			38		51. ( 4.3)24
53.				m500	55.			y15				57.				x25			59.			p25		61.			t18		63.		u14
65.				36a2	67.			625y4					69.					27a12b21						71. 8r6s9						73.		72c17
75.				6,400d41				77.			49a18					79.				t10			81. y9				83. 216a9b6
85.				n33	87.		660				89. 288b27										91.		c14			93.		432s16t13
				x15			25x2 ft2											3						5		105. 7						12
95.					97.								101.								103.									107.

																		4
	Chapter 8 Review															(page 696)

1.		a. 6b			b. xyz							c.		2t		2.			a. c d							d c
b. (r s) t								r (s t)								3.		a. factor							b. term
4.		a. 3			b.	1			5.		a. 16, 1, 25											b.		1	, 1		6. ﬁve hundred

																								2
less than m (answers may vary)																						7.		a. h 25						b.	100 2s
c.		1		t 6		d. 2 a2										8.		a. (n 4) in.									b. (b 4) in.
	2
														p
		a. (x 1) in.																						a. Let x
9.											b.				pounds							10.								weight of
														8
the volleyball (in ounces), 2x 2																							weight of the NBA
basketball (in ounces)																b.		22 oz					11. 72				12.		64		13. 40
14.			36		15.			28w					16.				24x			17.			2.08f				18. r
19.				5x 15			20.				2x 3 y											21.		3c 6
22.				12.6c 29.4							23. 7a, 9a									24.			2x2, 3x2; 2x, x
25.				9p	26.		7m					27.				4n			28.			p 18						29.		0.1k2
30.				8a3 1			31.				does not simplify													32. does not simplify
33.				w 34.		4h 15							35.					a. x				b. x				c.		4x 1
d.			4x 1			36.			(4x 4) ft									37.				yes		38.			no		39.		no
40.				no	41.		yes				42. yes							43.			equation							44.	true			45. 21
46.			32		47.		20.6						48.			107				49.			24			50.		2	51.		9
			7.8						0							16						2		56. 30.6								30
52.						53.						54.								55.										57.
																	5
58.			28		59.			3			60.		1.2						61.			4		62.		1		63.		20	64. 0.06
65.				They needed to borrow $97,750.																				66.			He originally had
725 patients. 67. The original cost was estimated to be
$27 million.							68.				There are 3,600 clients served by 45

A-50 Appendix V Answers to Selected Exercises

social workers. 69. It would take 6 hours for the hamburger to go from 71°F to 29°F. 70. It cost $32 to rent the trailer. 71. She runs 9 miles and she walks 6 miles. 72. The attendance on the ﬁrst day was 2,200 people. The attendance on the second day was 4,400 people. 73. The width of the parking lot is 25 feet and the length is 100 feet. 74. The lunar module was 54 feet tall. 75. a. base n, exponent 12

b. base 2x, exponent 6				c.	base r, exponent 4
d. base y 7, exponent 3					76.	a. m5 b. 3x4				c. a2b4
d. (pq)3		77. a. x4	b.	2x2 c. x3			d. does not simplify
78.	a. keep the base 3, don’t multiply the bases.									b. multiply
the exponents, don’t add them.						79.	712	80.	m2n3 81. y21
82.	81x4	83. 636	84.	b12		85. 256s10		86. 4.41x4y2
87.	( 9)15 88. a23		89. 8x15			90.	m10n18		91.	72a17
92.	x200	93. 256m13		94.	108t22

Chapter 8 Test

(page 706)

a. Variables

b. distributive

c. like

d. combined

coefﬁcient

f. substitute

g. expressions

h. equation

solve

check

2. a. (b c) d

b (c d)

1 t

t and t 1

s 10 the length of the trout

(in inches)

a. r 2

3xy

2w 7

three-fourths of t

h 5 the length of the upper

base (in feet)

2h 3

the length of the lower base (in

feet)

a. factor

b. term

4 terms

b. 1, 8, 1, 6

10.

11.

a. 36s

b. 120t

12x

d. 72m

12.

25x 5

b. 42 6x

c. 6y 4

d. 0.6a 0.9b

2.1

e. m 4

18r 9

13. 12m2 and 2m2

14.

12y

40a

21b2

11z 13

15.

3y 3

16.

It is not a solution.

17.

18.

3.1

19.

20.

21.

22.

23.

24.

25.

6.2

26. 1

27.

28.

15 29. The sound intensity of a jet engine is

110 decibels. 30.

At this time, the college has 2,080

parking spaces.

31.

The string section is made up of

54 musicians. 32. The developer donated 44 acres of land to the city. 33. The smaller number is 23 and the larger number is 40. 34. The width of the frame is 24 inches and

the length is 48 inches.		35.	a.	base: 6, exponent: 5
b. base: b, exponent: 4		36.	a.	2x2	b. x4	c. does not
simplify	d. x3 37. a. h6		b. m20		c. b8 d. x18
e. a6b10	f. 144a18b2	g. 216x15 h.			t15	38. Keep the

common base 5, and add the exponents. Do not multiply the common bases to get 25.

Chapters 1–8 Cumulative Review (page 708)

1. a. 7,535,700 b. 7,540,000 2. One billion, seven hundred twenty-six million, three hundred ﬁfty-seven thousand, sixty-eight; 1,000,000,000 700,000,000 20,000,000 6,000,000 300,000 50,000 7,000 60 8

3.	9,314 4. 3,322 5. 245,870 6. 875 7.						a.	260 ft
b.	4,000 ft2		8.	$170	9.	a. 1, 2, 4, 5, 10, 20	b.	22 5
10. a. 42			b. 7	11.	56	12. 2
13.

		−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6
		−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6

14.	a.	11				b.			11	c. false						15.				a. 5			b. 38
c. 240				d.				8	16.		125°F					17.			5			18.			200
19.	3	20.				45			21.		1		22.			2			23.			17	24.			12				25.		42	19

	8					54					7					5						18											22
26.	13			4		1			27.	a. He will have read													5	of the book.
	3					3																	6
b. He has				1			of the book left to read. 28. a. 1 hundredth

					6
b. 7		c. 3					d.		7 thousandths									e. 304.82							29.			658.04007
30.	182.894							31.		2,262					32.			3.16				33.			453.1					34. 13.60
35.	270 90								27 9				3			36.				67.5 mm					37.			a.			0.76
									7					9				$93.75								18.9						1	1	hr
b. 0.015				38.							39.				40.								41.								42.
													7																				3

																			1							21
43.	7.5 g			44.					about 16 lb							45.					, 25%, 0.3,								, 0.042

																				4							500
46.	52%			47.					65		48.		$37.20, $210.80										49.			820					50.	$556
51.	a. the 18–49 age group																b.		328 people							52.				mean: 6,
median: 5, mode: 10											53. 52								54.			a. x 4						b.		2w 50
55.	a. 15x								b. 28x2				56.			a. 6x 8									b.		15x 10y 20
57.	a.		5x			b.			12a2			c.	x y							d.		29x 36
58.	It is not a solution.												59.			5			60. 16							61.				4	62.		18

63.She must observe 21 more shifts.

64.The length is 84 feet and the width is 21 feet.

65.	a.	base: 8, exponent: 9	b.	base: a, exponent: 3
66.	a.	p9 b. t15 c. x5y7	d.	81a8 e. 108p12 f. ( 2.6)16

Study Set Section 9.1

(page 720)

point, line, plane

midpoint

5. angle

protractor

right

11.

180°

13.

Adjacent

15.

congruent

17.

90°

19.

a. one

b. line

b. S c. RST, TSR, S, 1

21.

a. SR, ST

23.

25.

130°

20°

50°

70°

27.

congruent

29.

a. false

b. false

c. false

d. true

31.

true

33. false

35.

line

37.

ray

39.

angle

41.

degree

43.

congruent

45.

a. T


47.	a. 2	b.	3	c.	1	d.	6	49.	50°		51.	25°		53.	75°
55.	130°	57.		right		59.	acute			61. straight				63.	obtuse
65.	10°	67.	27.5°			69.	70°	71.		65°	73.		30°, 60°, 120°
75.	25°, 115°, 65°				77. 60°			79.	75°		81.	a. true
b. false, a segment has two endpoints											c.	false, a line does

not have an endpoint d. false, point G is the vertex of the

angle

e. true f.

true 83. 40°

85.

135°

87.

a. 50°

b. 130°

c. 230°

d. 260°

89. a. 66°

156°

91. 141°

93.

1°

95.

a. about 80°

b. about 30°

about 65°

97.

a. 27°

b. 30°

103.

or 1

105.

	Study Set Section 9.2			(page 731)
1.	coplanar, noncoplanar			3. Perpendicular 5. alternate
7.	a.		l1 b.	l2
			l	l1
			2
9.	a.	l3	b.	l3
			l1	l
				1
			l2	l
				2

11.

corresponding

13. interior

15.

They are perpendicular.

17.

right 19.

perpendicular.

21. a. 1 and 5, 4 and

8, 2 and 6, 3 and 7

3, 4, 5, and 6

c. 3 and 5, 4 and 6

23.

m( 1)

130°, m( 2) 50°,

m( 3)

50°, m( 5)

130°, m( 6)

50°, m( 7)

50°,

m( 8)

130°

25. 1 X, 2 N

27. 12°, 40°, 40°

29.

10°, 50°, 130°

31.

a. 50°, 135°, 45°, 85° b. 180°

c. 180°

33.

vertical angles: 1 2; alternate interior angles:

B D, E A

35.

40°, 40°, 140°

37. 12°, 70°, 70°

39.

The plummet string should hang perpendicular to the

top of the stones.

41.

50°

43.

The strips of wallpaper

should be hung on the wall parallel to each other, and they

should be perpendicular to the ﬂoor.

45.

75°, 105°, 75°

55. 45%

yes

53.

57.

59.

	Study Set Section 9.3			(page 741)
1.	polygon	3. vertex	5.	equilateral, isosceles, scalene
7.	hypotenuse, legs 9.		addition
11. a.		b.		c.	d.
e.		f.		13. a.	b.
c.		d.		e.	f.

															Appendix V Answers to Selected Exercises																																																						A-51
					a. 90°									b. right												c.																					d.												e.									f.
15.					a. 90°									b. right												c.				AB,					BC												d.			AC									e.					AC				f.	AC
17.					a. isosceles																	b. converse																	19.									a.					EF							GF
b.			isosceles												21.							triangle										23.								AB											CB
25.					a. 4, quadrilateral, 4																										b. 6, hexagon, 6
27.					a. 7, heptagon, 7																						b. 9, nonagon, 9
29.					a. scalene															b. isosceles														31.											a. equilateral																					b. scalene
33.					yes						35.						no					37.					55°					39.							45°										41. 50°; 50°, 60°, 70°
43.			20°; 20°, 80°, 80°																					45.							68°								47.								9°									49.			39°						51.			44.75°
53.			28°								55.				73°							57.					90°						59.						45°											61.								90.7°							63.			61.5°
65.			12°								67.				52.5°									69.					39°, 39°, 102° or 70.5°, 70.5°, 39°
71.			73°								73.				75°							75.					a. octagon																					b. triangle																	c. pentagon
77.				As the jack is raised, the two sides of the jack remain the
same length.															79.							equilateral												85.										22						87. 40%															89.			0.10625
		Study Set Section 9.4																																(page 751)
		Study Set Section 9.4																																(page 751)
1.		hypotenuse, legs																						3.					Pythagorean																									5. a2, b2, c2
7.		right									9.				a.				BC						b.				AB							c.						AC								11.								64, 100, 100
13.					10 ft							15. 13 m												17.							73 mi													19.					137 cm
21.						4 cm						23.								80 m							25.					20 m												27.								19 m
					211 cm 3.32 cm																													2														m 14.42 m
29.					211 cm 3.32 cm																								31.					2							208							m 14.42 m
						90 in. 9.49 in.																											2											in. 4.47 in.
33.						90 in. 9.49 in.																							35.				2					20						in. 4.47 in.																					37.			no
																																															2														ft 127.28 ft
39.					yes						41.						12 ft							43.					25 in.										45.								2							16,200							ft 127.28 ft
47.				yes, 21,288 ft 35.89 ft																														53. no															55.							no						57.			no			59. no
		Study Set Section 9.5																																(page 761)
		Study Set Section 9.5																																(page 761)
1.		Congruent																	3.			congruent												5.											similar													7.				a. No, they are
different sizes.																				b. Yes, they have the same shape.
9.		PRQ										11. MNO															13. A B, Y T,
Z R,													YZ									TR,				AZ							BR,										AY													BT
15.					congruent														17.					angle, angle																				19.						100									21.						5.4
23.					proportional																	25.					congruent																				27.							is congruent to
29.					K																								M								H																														E
																													R																																						J
								,						,							D, B, C 33.																												a. B M,
31.					DF			,		AB				,		EF,					D, B, C 33.																												a. B M,
C N, D O,																												BC								MN									,	CD											NO					,	BD					MO
b. 72°								c.				10 ft									d.			9 ft							35.				yes, SSS															37.									not necessarily
39.					a. L H, M J, R E																																																					b. MR, LR, LM
c. HJ, JE, LR																			41.					yes							43.					not necessarily																										45.					yes
47.					not necessarily																			49.						yes				51.											not necessarily																						53. 8, 35
55.			60, 38									57.								true				59.							false: the angles must be between
congruent sides																						61. yes, SSS																	63.									yes, SAS														65.					yes, ASA
67.					not necessarily																			69.					80°, 2 yd															71.										19°, 14 m											73.			6 mm
75.			50°								77.						25					4			1				79.			16							81.										17.5 cm													83.					59.2 ft
75.			50°								77.				6							4							79.			16							81.										17.5 cm													83.					59.2 ft
															6									6
85.					36 ft							87. 34.8 ft															89.					1,056 ft																	93.							189						95.					21
		Study Set Section 9.6																																(page 773)
		Study Set Section 9.6																																(page 773)
1.		quadrilateral																				3.			rectangle														5.								rhombus															7.			trapezoid,
bases, isosceles																				9. a. four; A, B, C, D																																		b. four;
	AB			,		BC			,		CD				,			DA					c. two;									AC					,		BD										d. yes, no, no, yes
11.					a.		VU								b.							13.						a. right																b. parallel																		c. length
d. length													e. midpoint																		15.				rectangle																					17.						a. no						b. yes
c. no								d. yes											e. no									f. yes						19.													a. isosceles
b. J, M c. K, L d. M, L,																																																							ML

A-52

Appendix V Answers to Selected Exercises

21.

The four sides of the quadrilateral are the same length.

23.

the sum of the measures of the angles of a polygon; the

number of sides of the polygon

25.

a. square

b. rhombus

c. trapezoid

d. rectangle

27.

a. 90°

d. 18

29.

a. 42°

b. 95°

31. a. 9 b. 70° c. 110°

d. 110°

33.

2,160°

35.

3,240°

37.

1,080°

39.

1,800°

41.

43.

7 45. 13

47.

49.

a. 30°

b. 30°

c. 60°

8 cm

4 cm

51.

40°; m( A)

90°, m( B)

150°,

m( C)

40°, m( D)

80°

53. a. trapezoid

b. square

c. rectangle

d. trapezoid

e. parallelogram

55. 540°

61.

two hundred ﬁfty-four thousand, three hundred nine

63.

eighty-two million, four hundred ﬁfteen

Think It Through

(page 782)

about 108 ft2

Study Set Section 9.7

(page 786)

1. perimeter

3. area

5. area

8 ft 16 ft

128 ft2

9. a. p 4s, p 2l 2w

11.

c. d.


																b

				b
				b
13.	a rectangle and a triangle													15.		a. square inch							b. 1 m2
17.	32 in.				19.	23 mi				21.			62 in.			23.	94 in.				25. 15 ft
27.	5 m			29. 16 cm2						31.			6.25 m2			33.		144 in.2
35.	1,000,000 mm2 37.										27,878,400 ft2							39.		1,000,000 m2
41.	135 ft2				43.		11,160 ft2						45. 25 in.2					47.		27 cm2
49.	7.5 in.2				51.		10.5 mi2						53.	40 ft2			55.		91 cm2				57. 4 m
59.	12 cm				61.		36 m			63.			11 mi			65.	102 in.2				67.		360 ft2
69.	75 m2				71.		75 yd2				73. $1,200					75.		$4,875				77. length
15 in. and width 5 in.; length 16 in. and width 4 in. (answers
may vary)					79.		sides of length 5 m									81.		base 5 yd and
height 3 yd (answers may vary)														83. length 5 ft and width 4 ft;
length 20 ft and width 3 ft (answers may vary)																				85.		60 cm2
87.	36 m				89.	28		1	ft	91.			36 m		93.		x		3.7 ft, y				10.1 ft;
87.	36 m				89.	28			ft	91.			36 m		93.		x		3.7 ft, y				10.1 ft;
							3
50.8 ft			95. 80 1							81 trees				97.		vinyl			99.		$361.20
101.		$192			103. 111,825 mi2									105. 51 sheets							111. 6t
113.		2w 4					115.				5	x	117.		9r 16
113.		2w 4					115.				8	x	117.		9r 16
											8

Study Set Section 9.8

(page 798)

radius

3. diameter 5.

circumference 7. twice

OA, OC, OB 11. DA, DC, AC 13. ABC , ADC

15.

a. Multiply the radius by 2. b. Divide the diameter by 2.

17.

19.

square 6 21. arc AB 23. a. multiplication:

p r

b. raising to a power and multiplication: p r2

25.

8 ft 25.1 ft 27. 12 m 37.7 m 29. 50.85 cm


31.	31.42 in.	33. 9 in.2 28.3 in.2				35. 81 in.2 254.5 in.2
37.	128.5 cm2	39. 57.1 cm2			41. 27.4 in.2		43. 66.7 in.2
45.	50 yd 157.08 yd			47.	6 in. 18.8 in.
49.	20.25 mm2 63.6 mm2				51. a.	1 in.	b. 2 in.
c. 2 in. 6.28 in.			d. in.2 3.14 in.2
53.	mi2 3.14 mi2		55. 32.66 ft 102.60 ft
57.	13 times	59. 4 ft2 12.57 ft2; 0.25 ft2 0.79 ft2; 6.25%
65.	90% 67.	82.7%		69. 5.375¢ per oz			71. ﬁve

	Study Set Section 9.9																			(page 806)
1.	volume								3.				cone			5.		cylinder							7.		pyramid
9.	s														11.													13.				r
9.															11.													13.



																				h
																	Base


15.			cubic inches, mi3, m3															17.			a. perimeter									b. volume
c. area						d. volume										e. area						f. circumference 19. a. 50
b.		500			p	21.						a. cubic inch b.											1 cm3					23.		a right angle
b.		3			p	21.						a. cubic inch b.											1 cm3					23.		a right angle
25.		27				27.				1,000,000,000									29.				56 ft3					31.		125 in.3
33.			120 cm3								35. 1,296 in.3									37.				700 yd3					39.		32 ft3
41.			69.72 ft3									43.			6 yd3			45.		192 ft3 603.19 ft3
47.			3,150 cm3 9,896.02 cm3																					49.		39 m3 122.52 m3
51.			189 yd3 593.76 yd3																53.					288 in.3 904.8 in.3
55.			32		cm3 33.5 cm3													57.			486 in.3 1,526.81 in.3
55.			3		cm3 33.5 cm3													57.			486 in.3 1,526.81 in.3
59.			423 m3 1,357.17 m3																61.					60 cm3
63.			100 cm3 314.16 cm3																	65.				400 m3					67.		48 m3
69.			576 cm3								71. 180 cm3 565.49 cm3
73.		1		in.3					0.125 in.3								75. 2.125								77.			63 ft3 197.92 ft3

			8
79.			32,000					ft3 33,510.32 ft3																81.		8 1
79.								ft3 33,510.32 ft3																81.		8 1
					3
83.			a.		2,250 in.3 7,068.58 in.3																				b.	30.6 gal					89.	42
		4								1			or 1 5						2,400 mm
91.									93.								95.
91.									93.		5						95.
	Chapter 9 Review																	(page 811)
	Chapter 9 Review																	(page 811)
1.	points C and D, line CD, plane GHI																											2.		a.	6 units
b. E					c. yes								3. ABC, CBA, B, 1																	4.	a. acute
b. B										!					!
b. B					c.		BA and							BC			d. 48°					5.			1 and 2 are acute,
ABD and CBD are right angles, CBE is obtuse,
and ABC is a straight angle																						6.			yes			7.	yes
8.	a. obtuse angle														b. right angle										c. straight angle
d.		acute angle										9.			15°			10.	150°						11.			a. m( 1)				65°
b.		m( 2)							115°						12.		a. 39°						b. 90°					c. 51°			d.	51°
e.	yes				13.				a. 20°						b.		125°				c. 55°						14.		19°		15.	37°

16.No, only two angles can be supplementary.

17.a. parallel b. transversal c. perpendicular

18.4 and 6, 3 and 5 19. 1 and 5, 4 and 8, 2 and 6, 3 and 7 20. 1 and 3, 2 and 4, 5 and

7, and 6 and 8	21. m( 1)	m( 3) m( 5)
m( 7) 70°; m( 2)	m( 4)	m( 6) 110°

22.

m( 1)

60°, m( 2)

120°, m( 3)

130°, m( 4)

50°

23.

a. 40°

b. 50°, 50°

24.

a. 20°

b. 110°, 70°

25. a. 11°

b. 31°, 31°

26.

a. 23°

b. 82°, 82°

27.

a. 8, octagon, 8

b. 5, pentagon, 5

c. 3, triangle, 3

d. 6, hexagon, 6

e. 4, quadrilateral, 4

f. 10, decagon, 10

28.

a. isosceles,

b. scalene

c. equilateral

d. isosceles

29.

a. acute

b. right

obtuse

d. acute

30.

a. 90°

b. right

31.

90°

32.

50°

33.

71°

34.

18°; 36°, 28°, 116°

35.

50°

36.

56°

37.

67°

38.

83°

39.

13 cm

40. 17 ft

41.

36 in.

42. 20 ft

m 15.20 m

21,300 in. 36.06 in.

43.

231

44.

45.

73 in.

46.

21,023 in. 32 in.

47.

not a right triangle

48.

not a right triangle

49.

a. D

b. E

c. F

50.

a. 32°

b. 61°

6 in.

9 in.

51.

congruent, SSS

52.

congruent, SAS

53.

not necessarily congruent

54. congruent, ASA

55.

yes

56.

yes

57. 4, 28

58.

65 ft

59.

a. trapezoid

b. square

c. parallelogram

d. rectangle

e. rhombus

f. rectangle

60.

a. 15 cm

b. 40°

c. 100°

7.5 cm

e. 14 cm

61. a. true

b. true

c. true

d. false

62.

a. 65°

b. 115°

4 yd

63.

1,080°

64.

20 sides

65.

72 in.

66.

86 in.

67.

30 m

68.

36 m

69.

59 ft

70.

9 ft2

144 in.2

71.

9.61 cm2

72.

7,500 ft2

73.

450 ft2

74.

200 in.2

75. 120 cm2

76.

232 ft2

77.

152 ft2

78.

120 m2

79.

8 ft

80.

18 mm

81.

$3,281

82.

$4,608

83. a.

84. 21 ft 65.97 ft

85.

45.1 cm

86.

81 in.2 254.47 in.2

87.

130.3 cm2

88.

6,073.0 in.2

89.

125 cm3

90.

480 m3

91.

1,728 mm3

92.

500

in.3 523.60 in.3

93. 250 in.3 785.40 in.3

94.

2,000 yd3

95. 2,940 m3

96.

1,024

in.3 1,072.33 in.3

97.

1,518 ft3

98.

3.125 in.3 9.8 in.3

99.

1,728 in.3

100. 54 ft3

	Chapter 9 Test		(page 834)
1.	a. 135°, obtuse	b. 90°, right			c. 40°, acute
d.	180°, straight	2.	a. measure		b. length c. line
d.	complementary		3. D	4. a.	false	b. true	c. true
d.	true e. false	5.	20°; 60°, 60°		6.	133°
7.	a. transversal	b.	6	c. 7	8. m( 1)		155°,

m( 3)

155°, m( 4)

25°, m( 5)

25°, m( 6)

155°,

m( 7)

25°, m( 8)

155°

50°; 110°, 70°

10.

a. 8, octagon, 8

b. 5, pentagon, 5

c. 6, hexagon, 6

d. 4, quadrilateral, 4

11. a. isosceles

b. scalene

c. equilateral

d. isosceles

12.

70°

13.

84° 14.

a. 12

b. 13

c. 90°

d. 5

15. a.

b. 65°

c. 115° d. 115°

16.

1,440°

17. 118 in.

18.

15.2 m

19.

360 cm2

20.

$864

21.

144 in.2

22.

120 in.2

23. a.

24.

25. 21 ft 66.0 ft

26.

(40 12 ) ft 77.7 ft

27.

225 m2 706.9 m2

28.

R, S, T; RT,

29. a. congruent, SSS

b. congruent, ASA c. not necessarily congruent

congruent, SAS

30.

a. 8 in.

b. 50°

31.

yes

yes 32.

a. 6 m

12 m

33.

21 ft

34.

26 cm

in. 5.3 in.

in. 31.4 in.

36. 1,728 in.3

35.

986

37. 216 m3

38. 5,400 ft3

39.

1,296 in.3 4,071.50 in.3

											Appendix V Answers to Selected Exercises																																													A-53
40. 600 in.3										41. 1,890 ft3														42. 63 yd3 197.92 yd3																									43. 400 mi3
44.		256				in.3 268.08 in.3																				45.				11,250 ft3 35,343 ft3
44.		3				in.3 268.08 in.3																				45.				11,250 ft3 35,343 ft3
	Chapters 1–9 Cumulative Review																																									(page 838)
	Chapters 1–9 Cumulative Review																																									(page 838)
1.	$8,995							2.				2,110,000													3.	32,034								4.						11,022
5.	a.		602 ft									b.				19,788 ft2										6. 33 R 10														7.			48 gal
8.	a.		22 5 11															b. 1, 2, 3, 4, 6, 12																9.				a.		48						b.		8
10.		11		11.						a.					{. . . , 3, 2, 1, 0, 1, 2, 3, . . .}																																b.	3
12.		a. 12										b.			20							c. 64						d.		4						e. 16									f. 16
13.		$140								14.								2				15.			a.		5			b.					18					c.			8				d.			15
13.		$140								14.								2				15.			a.		4			b.				48						c.		9					d.	2
																		3							1					3														11								7
16.		9 oz						17.														18.					19.										20.											21.				142
16.		9 oz						17.									70					18.			6		19.			20							20.							20				21.				142			15
		38						9														3															3															8
22.								1							23.								ﬂuid oz							24. 13											cups					25.
22.		29						1	29						23.							32	ﬂuid oz							24. 13									4		cups					25.						9
26.		a.		3.1416											b.
c. six million, ﬁve hundred ten thousand, three hundred
forty-ﬁve and seven hundred ninety-eight thousandths
d.	7,000 400 90 8																									6							4									6									1

																										10						100								1,000								10,000
27.		145.188										28.						3,803.61								29.				25.6										30.				17.05
31.		0.053						32.							22.3125									33.			$2,712.50													34.					a. 899,708
b.	0.899708											35.						18,000 9											2,000								36.					9.32
																									7
37.		0.13						38.					a. 2									b.			7
37.		0.13						38.					a. 2									b.			9
39.								5					−											−0.1			2			3				2.89
39.								5							9												2			3										17
					–4 –										9												–			–										17
								8																			3			2

				−5 −4 −3 −2 −1 0 1 2 3 4 5
40.		a.		3				b.				1						41.				the smaller board																		42.				6		1					6.5

				7								4																																		2
43.		125,000										44.							75 ft					45.		a.			14 ft								b.				13.25 lb										13		1	lb
43.		125,000										44.							75 ft					45.		a.			14 ft								b.				13.25 lb										13			lb
																																																				4
c.	120 quarts													d.					750 min							46.				a.			1,538 g											b.			0.5 L
c.	0.000003 km																	47.				240 km					48.						a. about 4 m/gal
b.	11,370,000 L																	49.				about 4.5 kg												50.						167°F
		0.57,						57			, 0.1%.											1			, 33			1
51.								57														1						1	%, 0.3								52.						a.			93%						b. 7%
51.																											3		%, 0.3								52.						a.			93%						b. 7%
				100																1,000							3
53.		67.5						54.				120								55.				85%					56.					$205, $615
57.		$1,159.38													58.					500%					59.				$21					60. $1,567.50
61.		a.			380,000 vehicles																			b.		295,000 vehicles
c.	90,000 vehicles																			62.				a.	18%						b.			2,920,000
63.		a. food: about $17.5 billion																												b. about $2.2 billion
c. about $8.5 billion 64. mean: 0.86 oz, median: 0.855 oz,
mode: 0.85oz												65.								5			66. a.					2x 16											b.			75s 6
67.		a.			48a					b.					42b							68.			a.	27t 90												b. 32x 40y 8
69.		a.			3x				b.				6c2								c. 8m 6n													d. 12x 8
70.		It is not a solution.																						71.		24								72. 5								73.				89					74. 11
75.		She must make 7 more 6-hour classroom visits.
76.		a. base: 4, exponent: 8																								b. base: s, exponent: 4
77.		a. s10							b. a35												c. r5t9					d. 8b9c18												e. y22									f. ( 5.5)36
78.		a. acute											b. right											c. obtuse												d.	180°							79.					a. 75°
b. 15°				80.						a. 50°												b. 50°					c. 130°											d. 50°								81.					a. 75°
b. 30°							c. 105°												d.			105°			82.				46°, 134°											83.						73°
84.		26 m						85. yes														86.		42 ft					87.					540°						88.						48 m, 144 m2
89.		126 ft2								90. 91 in.2														91.			144 in.2										92.					circumference:

14 cm 43.98 cm, area: 49 cm2 153.94 cm2

A-54				Appendix V Answers to Selected Exercises
93.			98.31 yd2					94.		6,480 in.3							95.		972 in.3 3,053.63 in3
96.			48 m3 150.80 m3											97.			20 ft3 62.83 ft3
98.			1,728 in.3
		Appendix I							(page A-1)
		Appendix I							(page A-1)
	Fifty Addition Facts
1.		5	3.		7	5.		14		7.			12		9.		11		11.			9	13.			10		15.		7
17.			17	19.			7	21.			10			23.		18		25.			8		27.		13		29.		3
31.			8	33.		6		35.		8			37.		6		39.		10			41.		1		43.		8
45.			11	47.			15		49.			12
	Fifty Subtraction Facts
1.		3	3.		2	5.		4		7.			4	9.		9		11.		9		13.		6		15.		6		17.		2
19.			8	21.		9		23.		7			25.		8		27.		2		29.		9		31.		5		33.		6
35.			2	37.		5		39.		8			41.		1		43.		4		45.		7		47.		4		49.		7
	Fifty Multiplication Facts
1.		16		3.	18		5.		35				7.	10			9.	56			11.		9	13.			30		15.		15
17.			8	19.		0		21.		48			23.			0	25.			32		27.		9		29.		54
31.			0	33.		24		35.			12			37.		40		39.			28		41.			45		43.		21
45.			36	47.			25		49.			72
	Fifty Division Facts
1.		5	3.		2	5.		5		7.			5	9.		1		11.		9		13.		4		15.		0		17.		2
19.			1	21.		7		23.		9			25.		5		27.		3		29.		0		31.		3		33.		8
35.			7	37.		4		39.		7			41.		6		43.		4		45.		2		47.		1		49.		2
		Study Set Section II.1															(page A-7)
		Study Set Section II.1															(page A-7)
1.		monomial						3.	binomial							5.		binomial						7.		monomial
9.		monomial						11.		trinomial							13.		3			15. 2			17.		1		19.		7
21.			2, 2, 4, 4, 16						23.			13		25.			6	27.			31		29.			4	31.		1
33.			0 ft		35.		64 ft				37.			63 ft			39.		198 ft					43.		2
45.			3 11				47.		16			49.		6
			2		2

	Study Set Section II.2										(page A-12)
1.	like		3.	coefﬁcients, variables										5.		yes, 7y				7.	no
9.	yes, 13x3				11.		yes, 15x2				13. 2x2, 7x, 5x2								15. 9y
17.		12t2	19.			14s2		21.		9a	23.			5c	25. 7x 4
		7x2 7								8				3
27.					29.		12x3 149x						31. 8x2 2x 21
33.		8y2 4y 2						35.	6x2 x 5						37.		6.1a2 10a 19
39.		2n2 5			41.		5x2 x 11						43.		7x2 5x 1
45.		2x2 x 12.9						47.		16u3			49. 7x5				51.		19x2 5
53.		7x2 2x 5						55.	1.6a 8					57.	7b 4					59.	p2 2p
61. 1.7y2 3.1y 9								63.		5x2 6x 8						65. 12x2 13x 36
67.		x3 x 14						69. 12x				71.		(4x 8) ft						77.	0.8 oz
79.		54 ft
	Study Set Section II.3										(page A-19)

1.	monomials					3.		ﬁrst, outer, inner, last									5.		a. each, each
b.	any, third					7.	a.	6x2 x 12						b.		5x4 8ax2 3a2
9.	8, n3, 72n5					11. 2x, 5, 5, 4x, 15x, 11x											13. 12x5				15. 6b3
17.		6x5		19.			1 y7		21. 3x 12						23. 4t 28
25.		3x2 6x					2						29. 6x3 8x2 14x
						27. 6x4 2x3
31.		2p3 3p2 2p							33.		3q4 6q3 21q2
35.		a2 9a 20						37.	3x2 10x 8							39.		6a2 2a 20
41.		4x2 12x 9						43.		4x2 12x 9							45.		25t2 10t 1
47.		81b2 36b 4 49. 6x3 x2 1															51. x3 1
53.		x3 x2 5x 2							55. r4 5r3 2r2 7r 15
57.		4x2 11x 6						59.		12x2 14x 10								61.		x3 1
63.		12x3 17x2 6x 8									65.		(x2 4) ft2
67.		(6x2 x 1) cm2							69.		(35x2 43x 12) in.2
75.		four and ninety-one thousandths														77.		0.109375
79.		134.657			81.		10
	Study Set Appendix III												(page A-27)

1.	Inductive					3.	circular				5.	alternating						7.		alternating
9.	10 A.M.			11. 17				13.		27		15.		3	17.		17			19. R 21. e
23.					25.						27.									29.


																						4

31.		D	33.	Maria				35.		6 ofﬁce managers									37. 9 children
39.		I 41.		W		43.							45. K				47.		6	49. 3
51.		11	53.			9	55.		cage 3			57.		B, D, A, C
59.		18,935 respondants								61. 0

I N D E X

AAA similarity theorem, 759, 822 Absolute value, 136, 137, 193 Absolute value function

in expressions, 186, 200 symbol used for, 136

Acute angle, 715, 812 Acute triangle, 738, 818 Addend

decimals and, 331 deﬁned, 16

Addition

algebraic phrases of, 641 associative property of

deﬁned, 149

formula representing, 638, 696

uses for, 195

for whole numbers, 18, 19, 115

checking results, 18 commutative property of, 18,

115 deﬁned, 149

formula representing, 638, 696

uses for, 195

identity property of, 639 key words and phrases

indicating, 21, 116 writing symbols used for,

146 Addition property

of equality, 659, 700 of opposites, 150, 195

of zero, 19, 150, 195, 639 Addition symbol, 16 Additive identity, 150 Additive inverse, 150, 195 Adjacent angle, 716, 812 Algebraic expression. See

Expression Alternate interior angle

deﬁned, 727, 815 property of, 728 American system of

measurement, 443, 485 American units

of capacity, 449, 486 of length, 444, 485 of time, 450, 486

of weight, 447, 485 Amount, in percent sentences

deﬁned, 515, 574 identifying, 515

Amount-to-base ratio, 520 Angle

See also speciﬁc types classifying, 715, 812 complement of

deﬁned, 719

ﬁnding using algebra, 813

deﬁned, 714, 812 supplement of deﬁned, 719

ﬁnding using algebra, 813 of a trapezoid, 769

Approximation, 7

Arc of a circle, 793, 829 Area

deﬁned, 780, 826 units of, 827

Arithmetic, fundamental theorem of, 83

Arithmetic mean or average deﬁned, 107, 126, 367 ﬁnding, 107, 126

formula for, 609, 627 Associative property

of addition

formula representing, 638, 696

for integers, 149, 195

for whole numbers, 18, 19, 115

of multiplication

formula representing, 639 for integers, 168

for whole numbers, 45, 119 Average

deﬁned, 609 ﬁnding, 609

Axis, 595

Bar graph decimals and, 324 double, 596, 622 example of, 594 reading, 595, 622 triple, 596, 622

Base

in exponents, 85, 124

of an isosceles triangle, 738, 818 in percent sentences

deﬁned, 515, 574 identifying, 515

of a trapezoid, 769, 825

in volume formulas, 803, 831 Base angle, 738, 818

Base-10, 2 Bimodal, 615, 629 Braces, 2 Brackets, 105

Calculator adding with, 23

approximating volume with, 832

calculating helicopter landing pad paint costs with, 797

calculating revolutions of a tire with, 794

compounding interest with, 565

decimals and adding with, 332 dividing with, 363

multiplying with, 346 subtracting with, 334

dividing with, 64

entering negative numbers on, 151

exponential key of, 86 ﬁnding means with, 610 ﬁnding percents with, 517 ﬁnding perimeters of ﬁgures

that are combinations of polygons with, 779

ﬁnding the volume of a silo with, 805

ﬁnding the width of a TV screen with, 750

ﬁxed-point key of, 378 multiplying with, 48 negative numbers

dividing with, 180 multiplying with, 167 raising to a power, 171 subtracting with, 161

order of operations and parentheses and, 108

Pythagorean theorem and, 749, 820

solving proportions with, 435

square roots and approximating with, 390 ﬁnding with, 388

subtracting with, 35 Capacity

American units of, 449 American/metric

equivalencies, 473, 493 metric/American

equivalencies, 473, 493 unit conversion factor for,

449

Carrying, in addition, 16, 115 Celsius

conversion formula for, 474 measuring, 492

scale, 474

Change, ﬁnding in a quantity, 160, 196

Changing quantity, graphing, 600, 624

Chord, 792, 829 Circle

arc of, 793, 829 area of, 796, 830 center of, 792, 829 chord of, 793, 829

circumference of, 794, 829 deﬁned, 792, 829

radius of, 792, 829

Circle graph example of, 594

reading, 527, 576, 598, 623 Circumference

deﬁned, 793, 829

formulas for ﬁnding, 793, 829 Class interval, 601, 625 Coefﬁcient, 640, 697 Commission

amount of, 538, 579 formula for, 538, 579 rate of, 579

Common denominator, 242 Commutative property

of addition

formula representing, 638, 696

for integers, 149, 195

for whole numbers, 18, 115 of multiplication

formula representing, 639 for integers, 168

for whole numbers, 44, 119 Complementary angle, 718, 813 Complex fraction

deﬁned, 288, 309 simplifying, 288, 309

Composite number, 82, 123 Compound interest. See Interest,

compound

Cone, ﬁnding volume of, 802, 831 Congruency

alternate interior angles and, 728, 815

angles and, 715, 812 corresponding angles and, 815 isosceles trapezoids and, 770,

825

line segments and, 713, 812 parallelograms and, 769, 824 triangles and, 754, 822 vertical angles and, 717, 813

Congruent triangle

ASA property of, 756, 822 congruence properties of, 755,

822

corresponding parts of, 754, 822 deﬁned, 754, 822

properties of SAS, 755, 822 SSA, 756 SSS, 755, 822

Constant, 638, 696 Constant term, 640, 697 Corresponding angle

deﬁned, 726, 815

ﬁnding unknown measures of, 816

property of, 728 Credit (educational), 628 Credit hour, 612

I-1

I-2 Index

Cross product deﬁned, 430, 482 property of, 430

Cube, ﬁnding volume of, 802, 831 Cubic centimeter, 465, 489, 490 Cubic unit, 801, 831

Cylinder, ﬁnding volume of, 802, 831

Decimal

addends and, 331 adding

carrying and, 331, 398 estimating sums, 336, 398 process for, 331

signed, 335, 398

vertical form for, 330, 397 comparing

with another decimal, 321, 396 with a fraction, 378, 405

converting from words to standard form, 320, 395

deﬁned, 316 dividing

by another decimal, 360, 361, 402

by powers of 10, 364, 402, 403 signed, 364, 403

by a whole number, 358, 401 equivalency to fraction, 372, 404 expanded form of, 318, 395 expanded notation of, 318, 395 fractional part, 316, 395 graphing on a number line, 322,

396 graphs and, 324

as irrational numbers, 376 multiplying

estimating products, 351, 400 by powers of 10 greater than

1, 347, 399

by powers of 10 less than 1, 348, 399

process for, 344, 399 signed, 349, 400 vertical form for, 345

negative, 317, 321 number lines and, 378 as rational numbers, 376 reading, 319, 395 repeating

deﬁned, 373, 404 rounding, 376, 404

rounding, 322, 396 square root of, 388 square roots and

nonterminating, 390 standard form of, 317 standard notation of, 317 subtracting

borrowing and, 333, 398 estimating differences in,

336, 398 process for, 333

regrouping for, 333, 398 signed, 335, 398

vertical form for, 332, 397

in sums, 331 tables and, 324

terminating, 373, 404

whole number part, 316, 395 writing

as a percent, 506, 572 in words, 319, 395

Decimal equivalent, 372 Decimal notation, 316

Decimal numeration system, 316, 395

Decimal point, 316 Decimal quotient

estimating, 363, 402 rounding, 362, 402

Degree, as measure of an angle, 714

Degrees (temperature) Celsius

conversion formula for, 474

measuring, 492 scale, 474

Fahrenheit

conversion formula for, 474 measuring, 492

scale, 474 Denominator

of 0, 210, 297 of 1, 210, 297 common, 242

deﬁned, 208, 296, 308 least common. See Least

common denominator (LCD)

order of operations and, 102, 126, 183, 200

Diameter, 793, 829 Difference

decimals and, 332 deﬁned, 29

Digits, 2, 113 Discount

deﬁned, 544

formula for, 544, 580, 581 Discount rate, 544 Distributive property

deﬁned, 649

simplifying expressions with, 699

subtraction and, 650 Dividend, 54 Divisibility

deﬁned, 61 tests for, 61

Division

algebraic phrases of, 641 equality property of, 664,

700

key words and phrases indicating, 64, 121

long

form of, 358 process for, 56, 120

properties of

formula representing, 639 statement of, 55, 121

symbols used for, 54, 120

of whole numbers ending with zero, 62, 121

with zero, 56, 121 Division ladder, 84, 123 Divisor, 54

Double-bar graph, 596, 622

Endpoint, 713

English system of measurement, 443, 485

Equality

addition property of, 659, 700

division property of, 664, 700 multiplication property of,

662, 700

subtraction property of, 700 Equal-sized group

forming

solving by dividing fractions, 237, 301

solving by division, 179, 199 Equation

compared to expression, 658 deﬁned, 428, 658, 700 satisfying, 658

sides of, 658 solution of, 658, 700 solving

deﬁned, 659, 700

with multiple properties of equality, 668

simplifying expressions in, 671, 701

strategy for solving, 673, 701 Equiangular triangle, 737 Equilateral triangle, 737 Equivalent equations, 659, 700 Equivalent expressions, 648 Equivalent fractions

deﬁned, 211, 297 Estimation

front-end rounding addition and, 20, 116 multiplication and, 46, 119 subtraction and, 33, 117

with percents, 552, 582 of quotients, 62, 121

simplifying calculations using, 187, 200

Euclid, 712 Expanded form

of decimals, 318

of whole numbers, 4, 113 Expanded notation. See

Expanded form Exponent

deﬁned, 85, 124 natural-number

deﬁned, 688, 705 rules for, 693, 705

of one, 693 power rule for

deﬁned, 691

formula representing, 693, 705

product rule for deﬁned, 690

formula representing, 693, 705

Exponential expression deﬁned, 85, 689 evaluating, 85, 124

with decimal base, 349, 400 with fractional base, 224,

299

with negative bases, 169, 198 Exponential notation, 85 Expression

compared to equation, 658 deﬁned, 35, 639, 697 evaluating, 643, 697

containing fractions and decimals, 380, 405

containing square roots, 388, 407

deﬁned, 35, 118

in horizontal form, 35, 118 involving addition, 159, 196 involving multiple additions,

149, 195

involving subtraction, 159, 196

order of operations rule for, 102, 126

key words and phrases of, 641, 697

simplifying deﬁned, 648

distributive property and, 699

multiplication properties and, 648, 698

to solve equations, 671, 701 Extreme, in a proportion, 430,

482

Factor, 40, 80, 123 Factor tree, 83, 123 Fahrenheit

conversion formula for, 474 measuring, 492

scale, 474

Form of 1, 210, 297 Formula

complex fractions and, 287, 308 decimals and, 350, 365, 400 square roots and, 390, 407

Fraction adding

with different denominator, 245, 302

with same denominator, 242, 302

building deﬁned, 211

process for, 212, 297 comparing, 249, 303 comparing with decimal, 378,

405 complex

deﬁned, 288, 309 simplifying, 288, 309

			Index	I-3
in decimal notation	percents and amount of, 552	multiplying	Leg
deﬁned, 316	subtraction and, 33, 117	with like signs, 166, 197	of a right triangle, 747
repeating decimals and, 508,	Fundamental property of	nonzero, 167	of a trapezoid, 769, 825
572	fractions, 212	to solve repeated additions,	of a triangle, 738, 818
deﬁned, 208, 296		171, 198	Length
with different denominator	GCD. See Greatest common	with unlike signs, 165, 197	American units of, 444
adding, 245	divisor (GCD)	negative	American/metric
subtracting, 245	GCF. See Greatest common	deﬁned, 133, 137	equivalencies, 470, 491
dividing	factor (GCF)	multiplying, 169, 198	metric/American
like signed, 237, 301	Geometry	on number line, 193	equivalencies, 470, 491
rule for, 235, 300	deﬁned, 712, 811	powers of, 170, 198	preﬁxes for metric units of, 456
unlike signed, 236, 301	using algebraic concepts to	opposites, 137, 193	unit conversion factor for
equivalency to decimal, 372,	solve problems of, 716	positive, 133	American, 445
404	Grade point average (GPA),	subtracting, 156	metric, 458, 488
equivalent, 211, 297	ﬁnding, 612, 628	Interest	Like terms
fundamental property of, 212	Gram, 489	compound	combining, 653, 654, 699
graphing on a number line, 260,	Graph of a number, 5	deﬁned, 562, 585	deﬁned, 652, 699
304	Greatest common divisor	formula for, 565, 586	Line
greater than 1 as a percent, 507	(GCD), 96	time spans for computing,	coplanar, 725, 815
identifying the greater of two,	See also Greatest common	563, 585	deﬁned, 712
249, 303	factor (GCF)	deﬁned, 559, 584	parallel, 725, 726, 815
improper	Greatest common factor (GCF)	simple	perpendicular, 726, 815
converting from mixed	deﬁned, 95, 125	deﬁned, 560, 584	skew, 725
number, 259	ﬁnding using prime	formula for, 560, 584	Line graph, reading, 599, 623
deﬁned, 209, 297	factorization, 96, 125	Interest rate, 559	Line segment
writing as mixed number, 260	Grouping symbol	Interior angle	congruency of, 713, 812
lowest terms of, 213, 297	deﬁned, 104, 184	deﬁned, 815	deﬁned, 713, 812
multiplying	innermost pair, 106	examples of, 727	Liter, 464
process for, 211, 222, 298	key words and phrases	ﬁnding unknown measures of	Long division
signed, 222, 299	indicating, 105	with algebra, 815	form of, 358
simplifying answers, 223	outermost pair, 106	property of, 728	process for, 56, 120
three or more, 224		Inverse operation, 33, 55
negative, 209	Hemisphere, 809	Irregular shape, ﬁnding area of,	Mass
number lines and, 378	Histogram, 601, 624	784, 797, 827, 830	American/metric
of in problems using, 225, 299	Horizontal axis, 595, 622	Isosceles triangle	equivalencies, 471, 491
proper, 209, 297	Horizontal form	converse of theorem for, 739	deﬁned, 461, 489
as rational number, 211	for addition problems, 16	deﬁned, 737	metric/American
as repeating decimal, 507, 572	for multiplication problems, 40	parts of, 738, 818	equivalencies, 471, 491
with same denominator	for subtraction problems, 29	properties of, 818	preﬁxes for metric units of, 461
adding, 242	Hypotenuse	theorem for, 737	Mathematical statement,
subtracting, 242	deﬁned, 738, 818		converse of, 739, 750
signed	of a right triangle, 738, 747, 818	Key	Mean
multiplying, 222, 299		for bar graphs, 596	deﬁned, 107, 126, 627
subtracting, 243	Implied coefﬁcient, 640	for graphs, 622	ﬁnding, 107, 126, 609, 627
simplest form of, 213, 297	Improper fraction	for pictographs, 597	in a proportion, 430, 482
simplifying	converting from mixed		Means-extremes property, 430
process for, 214	number, 259, 304	LCD. See Least common	Measure of central tendency, 609,
steps of, 216, 297	deﬁned, 209, 297	denominator (LCD)	627
simplifying special forms of,	writing as mixed number, 260,	LCM. See Least common	Median
210	304	multiple (LCM)	deﬁned, 613
square root of, 388	Inequality	Least common denominator	ﬁnding, 613, 628
subtracting	strict, 136	(LCD)	Meter, 456, 488
with different denominator,	symbols used for, 136, 193	deﬁned, 244, 302	Metric preﬁx, 456, 488
245, 302	Inequality symbol	ﬁnding, 248	Metric system of measurement,
with same denominator, 242,	deﬁned, 6, 113	Least common multiple (LCM)	456
302	uses for, 5	deﬁned	Metric unit conversion factor
signed, 243	Integer	of denominators, 302	for capacity, 464, 489
undetermined, 210	absolute value of, 136	of two whole numbers, 90,	for length, 458, 488
uses for, 208	adding	91, 124	for mass, 462, 489
writing	like signed, 145, 194	ﬁnding	Metric units
as a decimal, 372, 374, 404	unlike signed, 147, 194	of denominators, 302	of capacity
as a percent, 506, 572	deﬁned, 133, 192	of fractions, 247	deﬁned, 464, 489
Fraction bar, 54	dividing	for larger numbers, 92	preﬁxes for, 464
Frequency polygon, 602, 625	signed, 176, 199	by listing multiples, 91, 125	of length
Front-end rounding	by zero, 178, 199	using prime factorization,	conversion chart for, 459,
addition and, 20, 116	graphing on a number line,	93, 125	460
multiplication and, 46, 119	133	of two whole numbers, 247	preﬁxes for, 456

I-4 Index

Metric units (continued) of mass

deﬁned, 462, 489 preﬁxes for, 461

of time, 450, 486 Midpoint, 713, 812 Minuend

decimals and, 333 deﬁned, 29

Mixed number adding

carrying and, 275, 307

as improper fractions, 271, 306

parts of, 272 simplifying fractional

answers of, 275 in vertical form, 307 in vertical from, 273

converting from improper fraction, 260, 304

deﬁned, 257, 304 dividing, 261, 305

graphing on a number line, 260, 304

improper fraction and, 304 multiplying, 261, 305

as shaded region, 257, 304 subtracting

borrowing and, 276, 307 as improper fractions, 306 in vertical form, 275, 307 writing in decimal form, 374,

404

writing as improper fraction, 259, 304

Modal value, 615 Mode, 615, 628

Money, rounding, 324, 396 Multiplication

algebraic phrases of, 641 associative property of

formula representing, 639 for integers, 168

for whole numbers, 45, 119 commutative property of

formula representing, 639 for integers, 168

for whole numbers, 44, 119 of fractions, 211

indications for

in expressions, 106

key words and phrases, 48 key words and phrases

indicating, 119

of multiple-digit numbers, 42 rules for integers, 167, 197 symbols used for, 40, 118, 638,

696

of whole numbers that end in zero, 41, 119

Multiplication property of 0

formula representing, 639 for integers, 168

for whole numbers, 45, 119

of 1

formula representing, 639 for fractions, 211

for integers, 168

for whole numbers, 45, 119 of equality, 662, 700

Negative fraction, 209 Negative integer. See Integer,

negative

Negative number, 132, 133, 192 Negative sign, 132

Negative symbol, 138, 193 Net gain, 188

Net income, 135 Net loss, 188 Number

composite, 123

ﬁnding 1 percent of, 552, 582 ﬁnding 2 percent of, 552 ﬁnding 5 percent of, 554, 583 ﬁnding 10 percent of, 552, 582 ﬁnding 15 percent of, 555, 583 ﬁnding 25 percent of, 554, 583 ﬁnding 50 percent of, 554, 583 ﬁnding percent of in multiples

of 10, 553, 582

ﬁnding percent of in multiples of 100, 556, 583

graphing, 5

mixed. See Mixed number multiples of, 89, 124 negative, 132, 133, 192 perfect, 89

positive, 132, 133, 192 prime, 123 prime-factored form of, 83 signed

deﬁned, 132

reversing the sign of, 158 whole. See Whole number

Number line

decimals and fractions on, 378, 405

integers on, 133

negative numbers on, 133, 192 whole numbers on, 5, 113

Numerator

of 0, 210, 297 deﬁned, 208, 296, 308

order of operations and, 102, 126, 183, 200

Obtuse angle, 715, 812 Obtuse triangle, 738, 818 One

as denominator, 210, 297 form of, 210, 297 multiplication property of

formula representing, 639 for fractions, 211

for integers, 168 Opposite number

adding pairs of, 151

addition property of, 150, 195 reading symbol used for, 138,

193

Opposite rule, opposite of, 137, 193

Order of operations rule decimals and, 350, 365, 403

for evaluating expressions, 102, 126

fractions and, 284, 308 multiple operations and, 183,

200

square roots and, 389 Origin on a number line, 5

Overbar and repeating decimals, 374

Parallel line, properties of, 728 Parallelogram

characteristics of as a rectangle, 769, 824

deﬁned, 767, 824 ﬁnding area of, 781, 826

Parentheses as grouping symbols, 115

Partial product, 44 Part-to-whole ratio, 520 Percent

applications of, 535 approximating with, 556, 583 circle graphs and, 527, 576 of decrease

deﬁned, 542, 580 ﬁnding, 539

method for solving, 542, 580 deﬁned, 500, 570

as equivalent fraction of whole numbers, 502, 503, 571

ﬁnding 1, 552, 582 ﬁnding 2, 552 ﬁnding 5, 554, 583 ﬁnding 10, 553, 582 ﬁnding 15, 555, 583 ﬁnding 25, 554, 583 ﬁnding 50, 554, 583

ﬁnding multiples of 10, 553, 582 ﬁnding multiples of 100, 556,

583

greater than 100%, 504, 571 of increase

deﬁned, 542, 580 ﬁnding, 539

method for solving, 542, 580 less than 1%, 506, 571

in percent sentences, 515 pie chart and, 527, 576 writing

as a decimal, 504, 572 as a fraction, 501, 571

mixed number as decimal, 505, 572

Percent equation deﬁned, 513

ﬁnding amounts with, 514, 574, 576

ﬁnding percents with, 515, 574 ﬁnding the base with, 518, 574 formula for, 515, 574 fractions vs. decimals in, 519,

574

Percent problem

rewriting facts of, 526, 576 types of, 513

Percent proportion deﬁned, 520

ﬁnding amounts with, 522, 575, 577

ﬁnding percents with, 523, 575 ﬁnding the base with, 525, 575 formula for, 521, 575

writing, 520, 575 Percent ratio, 520 Percent sentence, 513, 574 Perfect number, 89 Perfect square

deﬁned, 387, 406 square root of, 386

Perfect-square radicand, 387, 406 Perimeter

deﬁned, 22, 777, 826 ﬁnding, 116

units of, 827

Period in whole numbers, 2, 113 Pictograph, reading, 597, 622 Pie chart

example of, 594 reading, 527, 576

in volume formulas, 832 Place value

chart, 316, 317 chart for, 2, 113 identifying, 316

in whole numbers, 2, 113 Plane, 712

Point, 712

Polygon

	0	1	2	3	4	5	6	7	8	9
0	0	1	2	3	4	5	6	7	8	9
1	1	2	3	4	5	6	7	8	9	10
2	2	3	4	5	6	7	8	9	10	11
3	3	4	5	6	7	8	9	10	11	12
4	4	5	6	7	8	9	10	11	12	13
5	5	6	7	8	9	10	11	12	13	14
6	6	7	8	9	10	11	12	13	14	15
7	7	8	9	10	11	12	13	14	15	16
8	8	9	10	11	12	13	14	15	16	17
9	9	10	11	12	13	14	15	16	17	18

1.	3	2.	1	3.	2	4.	5
	2		1		5		4
5.	7	6.	1	7.	6	8.	9
	7		8		6		4
9.	3	10.	0	11.	6	12.	5
	8		4		3		1
13.	2	14.	4	15.	1	16.	7
	8		7		6		2
17.	8	18.	4	19.	7	20.	1
	9		3		0		3
21.	4	22.	8	23.	9	24.	5
	6		6		9		9
25.	0	26.	2	27.	7	28.	8
	8		2		6		8
29.	1	30.	4	31.	4	32.	5
	2		2		4		6
33.	3	34.	9	35.	2	36.	6
	3		7		6		9
37.	0	38.	8	39.	7	40.	5
	6		5		3		5
41.	1	42.	4	43.	3	44.	8
	0		1		5		4
45.	9	46.	3	47.	7	48.	1
	2		9		8		9
49.	5	50.	7
	7		1

1.	8	2.	8	3.	4	4.	4
	5		7		2		3
5.	7	6.	14	7.	12	8.	11
	3		7		8		5
9.	12	10.	10	11.	18	12.	8
	3		8		9		6
13.	10	14.	6	15.	15	16.	9
	4		3		9		5
17.	2	18.	10	19.	15	20.	10
	0		5		7		1
21.	17	22.	7	23.	13	24.	9
	8		1		6		0
25.	16	26.	12	27.	7	28.	11
	8		5		5		7
29.	14	30.	16	31.	5	32.	6
	5		7		0		4
33.	12	34.	14	35.	5	36.	11
	6		6		3		3
37.	13	38.	7	39.	9	40.	2
	8		0		1		1
41.	3	42.	9	43.	13	44.	11
	2		3		9		2
45.	10	46.	6	47.	4	48.	8
	3		1		0		4
49.	9	50.	5
	2		4

	0	1	2	3	4	5	6	7	8	9
0	0	0	0	0	0	0	0	0	0	0
1	0	1	2	3	4	5	6	7	8	9
2	0	2	4	6	8	10	12	14	16	18
3	0	3	6	9	12	15	18	21	24	27
4	0	4	8	12	16	20	24	28	32	36
5	0	5	10	15	20	25	30	35	40	45
6	0	6	12	18	24	30	36	42	48	54
7	0	7	14	21	28	35	42	49	56	63
8	0	8	16	24	32	40	48	56	64	72
9	0	9	18	27	36	45	54	63	72	81

1.	4	2.	1	3.	6	4.	9
	4		4		3		7
5.	5	6.	0	7.	5	8.	1
	7		8		2		2
9.	7	10.	4	11.	3	12.	9
	8		0		3		3
13.	5	14.	7	15.	3	16.	8
	6		2		5		8
17.	1	18.	3	19.	0	20.	6
	8		2		7		4
21.	8	22.	9	23.	6	24.	1
	6		9		0		3
25.	4	26.	8	27.	9	28.	7
	8		2		1		7
29.	9	30.	1	31.	9	32.	4
	6		5		0		5
33.	8	34.	7	35.	6	36.	7
	3		6		2		1
37.	5	38.	4	39.	7	40.	1
	8		3		4		1
41.	9	42.	2	43.	7	44.	2
	5		2		3		4
45.	6	46.	9	47.	5	48.	6
	6		2		5		1
49.	8	50.	9
	9		4


1.	4	20		2.	8	56		3.	3	6		4.	1	8
	9				7				5				3
5.	9	45		6.	7	42		7.	5	25		8.	3	24
	5				7				9				3
9.	5	5		10.	7		21	11.	9		81	12.	3		0
	8				6				9				2
13.	8		32	14.	6		18	15.	9		0	16.	2		10
	4				3				1				6
17.	4		8	18.	3		27	19.	1		1	20.	6		30
	1				4				7				5
21.	1		7	22.	4		16	23.	7		63	24.	5		0
	7				3				5				8
25.	7		35	26.	3		3	27.	5		15	28.	8		48
	7				2				3				6
29.	7		0	30.	2		16	31.	3		9	32.	6		12
	9				8				4				8
33.	9		72	34.	8		0	35.	4		28	36.	8		64
	6				6				7				7
37.	6		24	38.	6		54	39.	7		49	40.	7		14
	6				1				3				4
41.	6		36	42.	1		9	43.	3		12	44.	4		36
	2				8				2				1
45.	2		4	46.	8		40	47.	2		2	48.	1		4
	9				6
49.	9		18	50.	6		6


21.	1	a	3		a		5		a			22.		1	b	3		b		1	b
21.	8	a	8		a		8		a			22.		4	b	4		b		4	b
	2	2	1			2		2			2			4	3	1			3			3		3
23.		c				c				c			24.		d				d				d
	3			3				3						9			9					9
	3			3				3						9			9					9

I-6	Index
Weight		Whole number
	American units of, 447	adding, 15, 115
	American/metric	bar graphs and, 9, 114
	equivalencies, 471, 491	in decimal notation, 316
	deﬁned, 462	deﬁned, 2, 113
	metric/American	dividing, 54, 120
	equivalencies, 471, 491	even, 81, 123
	unit conversion factor for, 447	factoring, 80, 123
Weighted mean		inequality symbols and, 5,
	deﬁned, 611	113
	ﬁnding, 612, 628	line graphs and, 9, 114

mathematical key words,	tables and, 8, 114
phrases, and concepts	uses for, 208
for, 69	writing
multiplying, 40, 118	in expanded form, 4, 113
odd, 81, 123	in standard form, 2, 113
reading, 3, 113	in words, 3, 113
rounding
deﬁned, 6	Zero
process for, 7, 114	addition property of, 150, 195,
standard form of, 2, 113	639
subtracting, 29, 117	multiplication property of, 168,
	639

Area Formulas
square	A s2
rectangle	A lw
parallelogram	A bh
triangle	A 21 bh
trapezoid	A 1 h(b b			)
	2	1	2

	0	1	2	3	4	5	6	7	8	9
0	0	1	2	3	4	5	6	7	8	9
1	1	2	3	4	5	6	7	8	9	10
2	2	3	4	5	6	7	8	9	10	11
3	3	4	5	6	7	8	9	10	11	12
4	4	5	6	7	8	9	10	11	12	13
5	5	6	7	8	9	10	11	12	13	14
6	6	7	8	9	10	11	12	13	14	15
7	7	8	9	10	11	12	13	14	15	16
8	8	9	10	11	12	13	14	15	16	17
9	9	10	11	12	13	14	15	16	17	18

1.	3	2.	1	3.	2	4.	5
	2		1		5		4
5.	7	6.	1	7.	6	8.	9
	7		8		6		4
9.	3	10.	0	11.	6	12.	5
	8		4		3		1
13.	2	14.	4	15.	1	16.	7
	8		7		6		2
17.	8	18.	4	19.	7	20.	1
	9		3		0		3
21.	4	22.	8	23.	9	24.	5
	6		6		9		9
25.	0	26.	2	27.	7	28.	8
	8		2		6		8
29.	1	30.	4	31.	4	32.	5
	2		2		4		6
33.	3	34.	9	35.	2	36.	6
	3		7		6		9
37.	0	38.	8	39.	7	40.	5
	6		5		3		5
41.	1	42.	4	43.	3	44.	8
	0		1		5		4
45.	9	46.	3	47.	7	48.	1
	2		9		8		9
49.	5	50.	7
	7		1

1.	8	2.	8	3.	4	4.	4
	5		7		2		3
5.	7	6.	14	7.	12	8.	11
	3		7		8		5
9.	12	10.	10	11.	18	12.	8
	3		8		9		6
13.	10	14.	6	15.	15	16.	9
	4		3		9		5
17.	2	18.	10	19.	15	20.	10
	0		5		7		1
21.	17	22.	7	23.	13	24.	9
	8		1		6		0
25.	16	26.	12	27.	7	28.	11
	8		5		5		7
29.	14	30.	16	31.	5	32.	6
	5		7		0		4
33.	12	34.	14	35.	5	36.	11
	6		6		3		3
37.	13	38.	7	39.	9	40.	2
	8		0		1		1
41.	3	42.	9	43.	13	44.	11
	2		3		9		2
45.	10	46.	6	47.	4	48.	8
	3		1		0		4
49.	9	50.	5
	2		4

	0	1	2	3	4	5	6	7	8	9
0	0	0	0	0	0	0	0	0	0	0
1	0	1	2	3	4	5	6	7	8	9
2	0	2	4	6	8	10	12	14	16	18
3	0	3	6	9	12	15	18	21	24	27
4	0	4	8	12	16	20	24	28	32	36
5	0	5	10	15	20	25	30	35	40	45
6	0	6	12	18	24	30	36	42	48	54
7	0	7	14	21	28	35	42	49	56	63
8	0	8	16	24	32	40	48	56	64	72
9	0	9	18	27	36	45	54	63	72	81

1.	4	2.	1	3.	6	4.	9
	4		4		3		7
5.	5	6.	0	7.	5	8.	1
	7		8		2		2
9.	7	10.	4	11.	3	12.	9
	8		0		3		3
13.	5	14.	7	15.	3	16.	8
	6		2		5		8
17.	1	18.	3	19.	0	20.	6
	8		2		7		4
21.	8	22.	9	23.	6	24.	1
	6		9		0		3
25.	4	26.	8	27.	9	28.	7
	8		2		1		7
29.	9	30.	1	31.	9	32.	4
	6		5		0		5
33.	8	34.	7	35.	6	36.	7
	3		6		2		1
37.	5	38.	4	39.	7	40.	1
	8		3		4		1
41.	9	42.	2	43.	7	44.	2
	5		2		3		4
45.	6	46.	9	47.	5	48.	6
	6		2		5		1
49.	8	50.	9
	9		4


1.	4	20		2.	8	56		3.	3	6		4.	1	8
	9				7				5				3
5.	9	45		6.	7	42		7.	5	25		8.	3	24
	5				7				9				3
9.	5	5		10.	7		21	11.	9		81	12.	3		0
	8				6				9				2
13.	8		32	14.	6		18	15.	9		0	16.	2		10
	4				3				1				6
17.	4		8	18.	3		27	19.	1		1	20.	6		30
	1				4				7				5
21.	1		7	22.	4		16	23.	7		63	24.	5		0
	7				3				5				8
25.	7		35	26.	3		3	27.	5		15	28.	8		48
	7				2				3				6
29.	7		0	30.	2		16	31.	3		9	32.	6		12
	9				8				4				8
33.	9		72	34.	8		0	35.	4		28	36.	8		64
	6				6				7				7
37.	6		24	38.	6		54	39.	7		49	40.	7		14
	6				1				3				4
41.	6		36	42.	1		9	43.	3		12	44.	4		36
	2				8				2				1
45.	2		4	46.	8		40	47.	2		2	48.	1		4
	9				6
49.	9		18	50.	6		6


21.	1	a	3		a		5		a			22.		1	b	3		b		1	b
21.	8	a	8		a		8		a			22.		4	b	4		b		4	b
	2	2	1			2		2			2			4	3	1			3			3		3
23.		c				c				c			24.		d				d				d
	3			3				3						9			9					9
	3			3				3						9			9					9

cube	V s3
rectangular solid	V lwh
prism	V Bh
sphere	V 34 r3
cylinder	V r2h
cone	V 31 r2h
pyramid	V 31 Bh
	B represents the area of the base.

	0	1	2	3	4	5	6	7	8	9
0	0	1	2	3	4	5	6	7	8	9
1	1	2	3	4	5	6	7	8	9	10
2	2	3	4	5	6	7	8	9	10	11
3	3	4	5	6	7	8	9	10	11	12
4	4	5	6	7	8	9	10	11	12	13
5	5	6	7	8	9	10	11	12	13	14
6	6	7	8	9	10	11	12	13	14	15
7	7	8	9	10	11	12	13	14	15	16
8	8	9	10	11	12	13	14	15	16	17
9	9	10	11	12	13	14	15	16	17	18

1.	3	2.	1	3.	2	4.	5
	2		1		5		4
5.	7	6.	1	7.	6	8.	9
	7		8		6		4
9.	3	10.	0	11.	6	12.	5
	8		4		3		1
13.	2	14.	4	15.	1	16.	7
	8		7		6		2
17.	8	18.	4	19.	7	20.	1
	9		3		0		3
21.	4	22.	8	23.	9	24.	5
	6		6		9		9
25.	0	26.	2	27.	7	28.	8
	8		2		6		8
29.	1	30.	4	31.	4	32.	5
	2		2		4		6
33.	3	34.	9	35.	2	36.	6
	3		7		6		9
37.	0	38.	8	39.	7	40.	5
	6		5		3		5
41.	1	42.	4	43.	3	44.	8
	0		1		5		4
45.	9	46.	3	47.	7	48.	1
	2		9		8		9
49.	5	50.	7
	7		1

1.	8	2.	8	3.	4	4.	4
	5		7		2		3
5.	7	6.	14	7.	12	8.	11
	3		7		8		5
9.	12	10.	10	11.	18	12.	8
	3		8		9		6
13.	10	14.	6	15.	15	16.	9
	4		3		9		5
17.	2	18.	10	19.	15	20.	10
	0		5		7		1
21.	17	22.	7	23.	13	24.	9
	8		1		6		0
25.	16	26.	12	27.	7	28.	11
	8		5		5		7
29.	14	30.	16	31.	5	32.	6
	5		7		0		4
33.	12	34.	14	35.	5	36.	11
	6		6		3		3
37.	13	38.	7	39.	9	40.	2
	8		0		1		1
41.	3	42.	9	43.	13	44.	11
	2		3		9		2
45.	10	46.	6	47.	4	48.	8
	3		1		0		4
49.	9	50.	5
	2		4

	0	1	2	3	4	5	6	7	8	9
0	0	0	0	0	0	0	0	0	0	0
1	0	1	2	3	4	5	6	7	8	9
2	0	2	4	6	8	10	12	14	16	18
3	0	3	6	9	12	15	18	21	24	27
4	0	4	8	12	16	20	24	28	32	36
5	0	5	10	15	20	25	30	35	40	45
6	0	6	12	18	24	30	36	42	48	54
7	0	7	14	21	28	35	42	49	56	63
8	0	8	16	24	32	40	48	56	64	72
9	0	9	18	27	36	45	54	63	72	81

1.	4	2.	1	3.	6	4.	9
	4		4		3		7
5.	5	6.	0	7.	5	8.	1
	7		8		2		2
9.	7	10.	4	11.	3	12.	9
	8		0		3		3
13.	5	14.	7	15.	3	16.	8
	6		2		5		8
17.	1	18.	3	19.	0	20.	6
	8		2		7		4
21.	8	22.	9	23.	6	24.	1
	6		9		0		3
25.	4	26.	8	27.	9	28.	7
	8		2		1		7
29.	9	30.	1	31.	9	32.	4
	6		5		0		5
33.	8	34.	7	35.	6	36.	7
	3		6		2		1
37.	5	38.	4	39.	7	40.	1
	8		3		4		1
41.	9	42.	2	43.	7	44.	2
	5		2		3		4
45.	6	46.	9	47.	5	48.	6
	6		2		5		1
49.	8	50.	9
	9		4


1.	4	20		2.	8	56		3.	3	6		4.	1	8
	9				7				5				3
5.	9	45		6.	7	42		7.	5	25		8.	3	24
	5				7				9				3
9.	5	5		10.	7		21	11.	9		81	12.	3		0
	8				6				9				2
13.	8		32	14.	6		18	15.	9		0	16.	2		10
	4				3				1				6
17.	4		8	18.	3		27	19.	1		1	20.	6		30
	1				4				7				5
21.	1		7	22.	4		16	23.	7		63	24.	5		0
	7				3				5				8
25.	7		35	26.	3		3	27.	5		15	28.	8		48
	7				2				3				6
29.	7		0	30.	2		16	31.	3		9	32.	6		12
	9				8				4				8
33.	9		72	34.	8		0	35.	4		28	36.	8		64
	6				6				7				7
37.	6		24	38.	6		54	39.	7		49	40.	7		14
	6				1				3				4
41.	6		36	42.	1		9	43.	3		12	44.	4		36
	2				8				2				1
45.	2		4	46.	8		40	47.	2		2	48.	1		4
	9				6
49.	9		18	50.	6		6


21.	1	a	3		a		5		a			22.		1	b	3		b		1	b
21.	8	a	8		a		8		a			22.		4	b	4		b		4	b
	2	2	1			2		2			2			4	3	1			3			3		3
23.		c				c				c			24.		d				d				d
	3			3				3						9			9					9
	3			3				3						9			9					9