Multiplying Whole Numbers

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40	Chapter 1 Whole Numbers

Objectives

1Multiply whole numbers by one-digit numbers.

2Multiply whole numbers that end with zeros.

3Multiply whole numbers by two- (or more) digit numbers.

4Use properties of multiplication to multiply whole numbers.

5Estimate products of whole numbers.

6Solve application problems by multiplying whole numbers.

7Find the area of a rectangle.

S E C T I O N 1.4

Horizontal form

Vertical form

Multiplication of whole numbers is used by everyone. For example, to double a recipe, a cook multiplies the amount of each ingredient by two. To determine the ﬂoor space of a dining room, a carpeting salesperson multiplies its length by its width. An accountant multiplies the number of hours worked by the hourly pay rate to calculate the weekly earnings of employees.

1 Multiply whole numbers by one-digit numbers.

In the following display, there are 4 rows, and each of the rows has 5 stars.

4 rows

5 stars in each row

We can ﬁnd the total number of stars in the display by adding: 5 5 5 5 20. This problem can also be solved using a simpler process called multiplication.

Multiplication is repeated addition, and it is written using a multiplication symbol , which is read as “times.” Instead of adding four 5’s to get 20, we can multiply 4 and 5 to get 20.

Repeated addition	Multiplication
5 + 5 + 5 + 5	= 4 5 = 20	Read as “4 times 5 equals (or is) 20.”

We can write multiplication problems in horizontal or vertical form. The numbers that are being multiplied are called factors and the answer is called the product.

A raised dot and parentheses ( ) are also used to write multiplication in horizontal form.

Symbols Used for Multiplication

Symbol		Example
	times symbol	4	5
	raised dot	4	5
( )	parentheses	(4)(5) or 4(5) or (4)5

To multiply whole numbers that are less than 10, we rely on our understanding of basic multiplication facts. For example,

2 3 6, 8(4) 32, and 9 7 63

If you need to review the basic multiplication facts, they can be found in Appendix 1 at the back of the book.

1.4 Multiplying Whole Numbers

To multiply larger whole numbers, we can use vertical form by stacking them with their corresponding place values lined up. Then we make repeated use of basic multiplication facts.

EXAMPLE 1 Multiply: 8 47

Strategy We will write the multiplication in vertical form. Then, working right to left, we will multiply each digit of 47 by 8 and carry, if necessary.

WHY This process is simpler than treating the problem as repeated addition and adding eight 47’s.

Solution

To help you understand the process, each step of this multiplication is explained separately. Your solution need only look like the last step.

Tens column

Ones column


Vertical form	4 7
		8

We begin by multiplying 7 by 8.

4 7 Multiply 7 by 8. The product is 56.

8 Write 6 in the ones column of the answer,

6 and carry 5 to the tens column.

4 7

Multiply 4 by 8. The product is 32.

To the 32, add the carried 5 to get 37.8 Write 7 in the tens column and the

3 7 6 3 in the hundreds column of the answer.

The product is 376.

	5
Your solution should	47
look like this:	8
	376

2 Multiply whole numbers that end with zeros.

An interesting pattern develops when a whole number is multiplied by 10, 100, 1,000 and so on. Consider the following multiplications involving 8:

8 10		8	0		There is one zero in 10. The product is 8 with
					one 0 attached.
8 100		8	0	0	There are two zeros in 100. The product is 8 with
					two 0’s attached.
8 1	,000	8	,000		There are three zeros in 1,000. The product is 8 with
					three 0’s attached.
8 10	,000	8	0	,000	There are four zeros in 10,000. The product is 8 with
					four 0’s attached.

These examples illustrate the following rule.

Multiplying by 10, 100, 1,000, and So On

Self Check 1

Multiply: 6 54

Now Try Problem 19

To ﬁnd the product of a whole number and 10, 100, 1,000, and so on, attach the number of zeros in that number to the right of the whole number.

42	Chapter 1 Whole Numbers

Self Check 2

Multiply:

a.9 1,000

b.25 100

c.875(1,000)

Now Try Problems 23 and 25

Self Check 3

Multiply:

a.15 900

b.3,100 7,000

Now Try Problems 29 and 33

Self Check 4

Multiply: 36 334

Now Try Problem 37

EXAMPLE 2 Multiply: a. 6 1,000 b. 45 100 c. 912(10,000)

Strategy For each multiplication, we will identify the factor that ends in zeros and count the number of zeros that it contains.

WHY Each product can then be found by attaching that number of zeros to the other factor.

Solution

a.	6 1,000 6,000	Since 1,000 has three zeros, attach three 0’s after 6.
b.	45 100 4,500	Since 100 has two zeros, attach two 0’s after 45.
c.	912(10,000) 9,120,000	Since 10,000 has four zeros, attach four 0’s after 912.
c.	912(10,000) 9,120,000	Since 10,000 has four zeros, attach four 0’s after 912.

We can use an approach similar to that of Example 2 for multiplication involving any whole numbers that end in zeros. For example, to ﬁnd 67 2,000, we have

67 2,000 67 2 1,000	Write 2,000 as 2 1,000.
134 1,000	Working left to right, multiply 67 and 2 to get 134.
134,000	Since 1,000 has three zeros, attach three 0’s
	after 134.

This example suggests that to ﬁnd 67 2,000 we simply multiply 67 and 2 and attach three zeros to that product. This method can be extended to ﬁnd products of two factors that both end in zeros.

EXAMPLE 3 Multiply: a. 14 300 b. 3,500 50,000

Strategy We will multiply the nonzero leading digits of each factor. To that product, we will attach the sum of the number of trailing zeros in the factors.

WHY This method is faster than the standard vertical form multiplication of factors that contain many zeros.

Solution

a. The factor 300 has two trailing zeros.

14 300 4,200 Attach two 0’s after 42.		1
14 300 4,200 Attach two 0’s after 42.		14
		3
		3
		42
Multiply 14 and 3
Multiply 14 and 3
	to get 42.

b.The factors 3,500 and 50,000 have a total of six trailing zeros.

3,500 50,000 175,000,000 Attach six 0’s after 175.		2
3,500 50,000 175,000,000 Attach six 0’s after 175.		35
		5
		5
		175
	Multiply 35 and 5
	Multiply 35 and 5
	to get 175.
	to get 175.

Success Tip Calculations that you cannot perform in your head should be shown outside the steps of your solution.

3 Multiply whole numbers by two- (or more) digit numbers.

EXAMPLE 4 Multiply: 23 436

Strategy We will write the multiplication in vertical form. Then we will multiply 436 by 3 and by 20, and add those products.

WHY Since 23 3 20, we can multiply 436 by 3 and by 20, and add those products.

1.4 Multiplying Whole Numbers

Solution

Each step of this multiplication is explained separately. Your solution need only look like the last step.

Hundreds column

Tens column

Ones column


Vertical form	4 3 6		Vertical form multiplication is often
		2 3	easier if the number with the larger
			amount of digits is written on top.

We begin by multiplying 436 by 3.

4 3 6

2 3

1 1

4 3 6

2 3

0 8

1		1
	4 3		6
		2	3

1 3 0 8

Multiply 6 by 3. The product is 18. Write 8 in the ones column and carry 1 to the tens column.

Multiply 3 by 3. The product is 9. To the 9, add the carried 1 to get 10. Write the 0 in the tens column and carry the 1 to the hundreds column.

Multiply 4 by 3. The product is 12. Add the 12 to the carried 1 to get 13. Write 13.

We continue by multiplying 436 by 2 tens, or 20. If we think of 20 as 2 10, then we simply multiply 436 by 2 and attach one zero to the result.

1 1

4 3 6

2 3

13 0 8

2 0

1 1

4 3 6

2 3

13 0 8

7 2 0

		1
	1	1
	4	3	6
		2	3

1 3 0 8
8 7 2 0
		1
	1	1
	4 3 6
		2 3
1	3 0 8
8	7 2 0

1 0, 0 2 8

Write the 0 that is to be attached to the result of 20 436 in the ones column (shown in blue). Then multiply 6 by 2. The product is 12. Write 2 in the tens column and carry 1.

Multiply 3 by 2. The product is 6. Add 6 to the carried 1 to get 7. Write the 7 in the hundreds column. There is no carry.

Multiply 4 by 2. The product is 8. There is no carried digit to add. Write the 8 in the thousands column.

Draw another line beneath the two completed rows. Add column by column, working right to left. This sum gives the product of 435 and 23.

The product is 10,028.

44	Chapter 1 Whole Numbers

The Language of Mathematics In Example 4, the numbers
The Language of Mathematics In Example 4, the numbers				4 3 6
1,308 and 8,720 are called partial products. We added the				2 3
partial products to get the answer, 10,028. The word partial		1		3 0 8
means only a part, as in a partial eclipse of the moon.			8	7 2 0
	1 0, 0 2 8

Self Check 5

Multiply:

a.706(351)

b.4,004(2,008)

Now Try Problem 41

When a factor in a multiplication contains one or more zeros, we must be careful to enter the correct number of zeros when writing the partial products.

EXAMPLE 5 Multiply: a. 406 253 b. 3,009(2,007)

Strategy We will think of 406 as 6 400 and 3,009 as 9 3,000.

WHY Thinking of the multipliers (406 and 3,009) in this way is helpful when determining the correct number of zeros to enter in the partial products.

Solution

We will use vertical form to perform each multiplication.

a.Since 406 6 400, we will multiply 253 by 6 and by 400, and add those partial products.

253
406
1 518	d	6 253
101 200	d	400 253. Think of 400 as 4 100 and simply multiply 253 by 4
102,718		and attach two zeros (shown in blue) to the result.

The product is 102,718.

b.Since 3,009 9 3,000, we will multiply 2,007 by 9 and by 3,000, and add those partial products.

2,007
3,009
18 063	d	9 2,007
6 021 000	d	3,000 2,007. Think of 3,000 as 3 1,000 and simply multiply
6,039,063		2,007 by 3 and attach three zeros (shown in blue) to the result.

The product is 6,039,063.

4 Use properties of multiplication to multiply whole numbers.

Have you ever noticed that two whole numbers can be multiplied in either order because the result is the same? For example,

4 6 24 and 6 4 24

This example illustrates the commutative property of multiplication.

Commutative Property of Multiplication

The order in which whole numbers are multiplied does not change their product.

For example,

7 5 5 7

1.4 Multiplying Whole Numbers

Whenever we multiply a whole number by 0, the product is 0. For example,

0 5 0, 0 8 0, and 9 0 0

Whenever we multiply a whole number by 1, the number remains the same. For example,

3 1 3, 7 1 7, and 1 9 9

These examples illustrate the multiplication properties of 0 and 1.

Multiplication Properties of 0 and 1

The product of any whole number and 0 is 0.

The product of any whole number and 1 is that whole number.

Success Tip If one (or more) of the factors in a multiplication is 0, the product will be 0. For example,

16(27)(0) 0

and

109 53 0 2 0

To multiply three numbers, we ﬁrst multiply two of them and then multiply that result by the third number. In the following examples, we multiply 3 2 4 in two ways. The parentheses show us which multiplication to perform ﬁrst. The steps of the solutions are written in horizontal form.

The Language of Mathematics In the following example, read (3 2) 4 as “The quantity of 3 times 2,” pause slightly, and then say “times 4.” We read

3 (2 4) as “3 times the quantity of 2 times 4.” The word quantity alerts the reader to the parentheses that are used as grouping symbols.

Method 1: Group 3 2

(3 2) 4 6 4		Multiply 3 and 2 to
		get 6.
24		Multiply 6 and 4 to
		get 24.

		Same result

Method 2: Group 2 4

3 (2 4) 3 8	Then multiply 2 and 4
	to get 8.
24	Then multiply 3 and 8
	to get 24.

Either way, the answer is 24.This example illustrates that changing the grouping when multiplying numbers doesn’t affect the result. This property is called the associative property of multiplication.

Associative Property of Multiplication

The way in which whole numbers are grouped does not change their product. For example,

(2 3) 5 2 (3 5)

Sometimes, an application of the associative property can simplify a calculation.

EXAMPLE 8

Daily Pay

Do the multiplication within the parentheses ﬁrst. Since 100 has two zeros, attach two 0’s after 17.

Use the associative property of multiplication to regroup the factors.

46	Chapter 1 Whole Numbers

Self Check 6

Find the product: (23 25) 4

Now Try Problem 45

EXAMPLE 6 Find the product: (17 50) 2

Strategy We will use the associative property to group 50 with 2.

WHY It is helpful to regroup because 50 and 2 are a pair of numbers that are easily multiplied.

Solution

We will write the solution in horizontal form. (17 50) 2 17 (50 2)

17 100

1,700

Self Check 7

Estimate the product: 74 488

Now Try Problem 51

Self Check 8

DAILY PAY In 2008, the average U.S. construction worker made $22 per hour. At that rate, how much money was earned in an 8-hour workday? (Source:

Bureau of Labor Statistics)

Now Try Problem 86

5 Estimate products of whole numbers.

Estimation is used to ﬁnd an approximate answer to a problem.

EXAMPLE 7 Estimate the product: 59 334

Strategy We will use front-end rounding to approximate the factors 59 and 334. Then we will ﬁnd the product of the approximations.

WHY Front-end rounding produces whole numbers containing many 0’s. Such numbers are easier to multiply.

Solution

Both of the factors are rounded to their largest place value so that all but their ﬁrst digit is zero.

Round to the nearest ten.

59 334

60 300

Round to the nearest hundred.

To ﬁnd the product of the approximations, 60 300, we simply multiply 6 by 3, to get 18, and attach 3 zeros. Thus, the estimate is 18,000.

If we calculate 59 334, the product is exactly 19,706. Note that the estimate is close: It’s only 1,706 less than 19,706.

6 Solve application problems by multiplying whole numbers.

Application problems that involve repeated addition are often more easily solved using multiplication.

In 2008, the average U.S. manufacturing worker made $18 per hour. At that rate, how much money was earned in an 8-hour workday? (Source: Bureau of Labor Statistics)

Strategy To ﬁnd the amount earned in an 8-hour workday, we will multiply the hourly rate of $18 by 8.

WHY For each of the 8 hours, the average manufacturing worker earned $18. The amount earned for the day is the sum of eight 18’s: 18 18 18 18 18 18 18 18. This repeated addition can be calculated more simply by multiplication.

Solution

We translate the words of the problem to numbers and symbols.

EXAMPLE 9

1.4 Multiplying Whole Numbers

The amount earned in
The amount earned in	is equal to	the rate per hour	times	8 hours.
an 8-hr workday
an 8-hr workday
The amount earned in		18		8
an 8-hr workday		18		8
an 8-hr workday

Use vertical form to perform the multiplication:

8 144

In 2008, the average U.S. manufacturing worker earned $144 in an 8-hour workday.

We can use multiplication to count objects arranged in patterns of neatly arranged rows and columns called rectangular arrays.

The Language of Mathematics An array is an orderly arrangement. For example, a jewelry store might display a beautiful array of gemstones.

Pixels Refer to the illustration at the right. Small dots of color, called pixels, create the digital images seen on computer screens. If a 14-inch screen has 640 pixels from side to side and 480 pixels from top to bottom, how many pixels are displayed on the screen?

Pixel

R G

R G B R G

G B R G B R B R G B R G B G B R G B R R G B R G

R G

Strategy We will multiply 640 by 480 to determine the number of pixels that are displayed on the screen.

WHY The pixels form a rectangular array of 640 rows and 480 columns on the screen. Multiplication can be used to count objects in a rectangular array.

Solution

We translate the words of the problem to numbers and symbols.

The number of pixels	is equal to	the number of	times	the number of
on the screen		pixels in a row		pixels in a column.
The number of pixels		640		480
on the screen

To ﬁnd the product of 640 and 480, we use vertical form to multiply 64 and 48 and attach two zeros to that result.

4864 192 2 880

3,072

Since the product of 64 and 48 is 3,072, the product of 640 and 480 is 307,200. The screen displays 307,200 pixels.

Self Check 9

PIXELS If a 17-inch computer screen has 1,024 pixels from side to side and 768 from top to bottom, how many pixels are displayed on the screen?

Now Try Problem 93

Weight Lifting

EXAMPLE 10

48	Chapter 1 Whole Numbers

The Language of Mathematics Here are some key words and phrases that are often used to indicate multiplication:

double

triple

twice

times

Self Check 10

INSECTS Leaf cutter ants can carry pieces of leaves that weigh 30 times their body weight. How much can an ant lift if it weighs 25 milligrams?

Now Try Problem 99

In 1983, Stefan Topurov of Bulgaria was the ﬁrst man to lift three times his body weight over his head. If he weighed 132 pounds at the time, how much weight did he lift over his head?

Strategy To ﬁnd how much weight he lifted over his head, we will multiply his body weight by 3.

WHY We can use multiplication to determine the result when a quantity increases in size by 2 times, 3 times, 4 times, and so on.

Solution

We translate the words of the problem to numbers and symbols.

The amount he

lifted over his head was 3 times his body weight.

The amount he		132
= 3		132
lifted over his head

Use vertical form to perform the multiplication:

132

3 396

Stefan Topurov lifted 396 pounds over his head.

Using Your CALCULATOR The Multiplication Key: Seconds in a Year

There are 60 seconds in 1 minute, 60 minutes in 1 hour, 24 hours in 1 day, and 365 days in 1 year. We can ﬁnd the number of seconds in 1 year using the multiplication key on a calculator.

60 60 24 365

31536000

One some calculator models, the ENTER key is pressed instead of the for the result to be displayed.

There are 31,536,000 seconds in 1 year.

7 Find the area of a rectangle.

One important application of multiplication is ﬁnding the area of a rectangle.The area of a rectangle is the measure of the amount of surface it encloses. Area is measured in square units, such as square inches (written in.2) or square centimeters (written cm2), as shown below.

		1 in.
					1 cm
1 in.			1 in.	1 cm		1 cm
1 in.			1 in.	1 cm		1 cm

					1 cm

		1 in.
	One square inch (1 in.2 )			One square centimeter (1 cm2 )

1.4 Multiplying Whole Numbers

The rectangle in the ﬁgure below has a length of 5 centimeters and a width of 3 centimeters. Since each small square region covers an area of one square centimeter, each small square region measures 1 cm2.The small square regions form a rectangular pattern, with 3 rows of 5 squares.

3 centimeters								One square centimeter
3 centimeters
(cm)
(cm)								(1 cm2 )

5 cm

Because there are 5 3, or 15, small square regions, the area of the rectangle is 15 cm2.This suggests that the area of any rectangle is the product of its length and its width.

Area of a rectangle length width

By using the letter A to represent the area of the rectangle, the letter l to represent the length of the rectangle, and the letter w to represent its width, we can write this formula in simpler form. Letters (or symbols), such as A, l, and w, that are used to represent numbers are called variables.

Area of a Rectangle

The area, A, of a rectangle is the product of the rectangle’s length, l, and its width, w.

Area length width or A l w

The formula can be written more simply without the raised dot as A lw.

EXAMPLE 11	Gift Wrapping When completely unrolled, a long sheet

of gift wrapping paper has the dimensions shown below. How many square feet of gift wrap are on the roll?

3 ft

12 ft

Strategy We will substitute 12 for the length and 3 for the width in the formula for the area of a rectangle.

WHY To ﬁnd the number of square feet of paper, we need to ﬁnd the area of the rectangle shown in the ﬁgure.

Solution

We translate the words of the problem to numbers and symbols.

The area of	is equal to	the length of	times	the width of
the gift wrap	is equal to	the roll	times	the roll.
The area of	=	12		3
the gift wrap	=	12		3
the gift wrap
	=	36

There are 36 square feet of wrapping paper on the roll. This can be written in more compact form as 36 ft2.

Self Check 11

ADVERTISING The rectangular posters used on small billboards in the New York subway are 59 inches wide by 45 inches tall. Find the area of a subway poster.

Now Try Problems 53 and 55

50	Chapter 1 Whole Numbers

Caution! Remember that the perimeter of a rectangle is the distance around it and is measured in units such as inches, feet, and miles. The area of a rectangle is the amount of surface it encloses and is measured in square units such as in.2, ft2, and mi2.

ANSWERS TO SELF CHECKS
ANSWERS TO SELF CHECKS
1.	324 2.	a.	9,000 b.		2,500	c. 875,000	3. a.	13,500 b.	21,700,000
4.	12,024	5.	a.	247,806	b. 8,040,032 6.		2,300	7. 35,000	8. $176
9.	786,432	10.		750 milligrams		11. 2,655 in.2

STUDY SKILLS CHECKLIST

Get the Most from Your Textbook

The following checklist will help you become familiar with some useful features in this book.

Place a check mark in each box after you answer the question.

Locate the Deﬁnition for divisibility on page 61 and the Order of Operations Rules on page 102. What color are these boxes?

Find the Caution box on page 36, the Success Tip box on page 45, and the Language of Mathematics box on page 45. What color is used to identify these boxes?

Each chapter begins with From Campus to Careers (see page 1). Chapter 3 gives information on how to become a school guidance counselor. On what page does a related problem appear in Study Set 3.4?

Locate the Study Skills Workshop at the beginning of your text beginning on page S-1. How many Objectives appear in the Study Skills Workshop?

Answers:Green,Red,255,7

S E C T I O N 1.4 STUDY SET

VOCABULARY

Fill in the blanks.

1.In the multiplication problem shown below, label each factor and the product.

	5	10 50



2.	Multiplication is			addition.
3.	The		property of multiplication states that

the order in which whole numbers are multiplied does not change their product. The

property of multiplication states that the way in which whole numbers are grouped does not change their product.

4. Letters that are used to represent numbers are called

5.If a square measures 1 inch on each side, its area is 1 inch.

6. The of a rectangle is a measure of the amount of

surface it encloses.

CONCEPTS

7.a. Write the repeated addition 8 8 8 8 as a multiplication.

b.Write the multiplication 7 15 as a repeated addition.

8. a. Fill in the blank: A rectangular		of red
squares is shown below.

b.Write a multiplication statement that will give the number of red squares.

46. (29 2) 50

48. 250 (4 289)

9.a. How many zeros do you attach to the right of 25 to ﬁnd 25 1,000?

b.How many zeros do you attach to the right of 8 to ﬁnd 400 . 2,000?

10.a. Using the numbers 5 and 9, write a statement that illustrates the commutative property of multiplication.

b.Using the numbers 2, 3, and 4, write a statement that illustrates the associative property of multiplication.

11.Determine whether the concept of perimeter or that of area should be applied to ﬁnd each of the following.

a.The amount of ﬂoor space to carpet

b.The number of inches of lace needed to trim the sides of a handkerchief

c.The amount of clear glass to be tinted

d.The number of feet of fencing needed to enclose a playground

12.Perform each multiplication.

a.	1 25	b.	62(1)
c.	10 0	d.	0(4)

NOTATION

13.Write three symbols that are used for multiplication.

14.What does ft2 mean?

15.Write the formula for the area of a rectangle using variables.

16.Which numbers in the work shown below are called partial products?

8623 258 1 720

1,978

GUIDED PRACTICE

Multiply. See Example 1.

17.	15 7	18.	19 9
19.	34 8	20.	37 6

Perform each multiplication without using pencil and paper or a calculator. See Example 2.

21.	37 100	22.	63 1,000
23.	75 10	24.	88 10,000
25.	107(10,000)	26.	323(100)
27.	512(1,000)	28.	673(10)

		1.4	Multiplying Whole Numbers		51
Multiply. See Example 3.
29.	68	40	30.	83 30
31.	56	200	32.	222 500
33.	130(3,000)		34.	630(7,000)
35.	2,700(40,000)		36.	5,100(80,000)
Multiply. See Example 4.
37.	73	128	38.	54 173
39.	64(287)		40.	72(461)
Multiply. See Example 5.
41.	602 679		42.	504 729
43.	3,002(5,619)		44.	2,003(1,376)

Apply the associative property of multiplication to ﬁnd the product. See Example 6.

45. (18 20) 5

47. 250 (4 135)

Estimate each product. See Example 7.

49.	86 249	50.	56 631
51.	215 1,908	52.	434 3,789

Find the area of each rectangle or square. See Example 11.

53.		6 in.				54.
		6 in.
									50 m
				14 in.					50 m
				14 in.

							22 m
55.				12 in.		56.		20 cm
55.						56.


							20 cm

			12 in.
	TRY IT YOURSELF
	TRY IT YOURSELF
Multiply.
57.		213			58.	863
57.		7			58.	9
59.		34,474 2			60.	54,912 4
61.		99			62.	73
61.		77			62.	59

52	Chapter 1	Whole Numbers
63.	44(55)(0)	64.	81 679 0 5
65.	53 30	66.	20 78
67.	754	68.	846
67.	59	68.	79
69.	(2,978)(3,004)	70.	(2,003)(5,003)
71.	916	72.	889
71.	409	72.	507
73.	25 (4 99)	74.	(41 5) 20
75.	4,800 500	76.	6,400 700
77.	2,779	78.	3,596
77.	128	78.	136
79.	370 450	80.	280 340

APPLICATIONS

81.BREAKFAST CEREAL A cereal maker advertises “Two cups of raisins in every box.” Find the number of cups of raisins in a case of 36 boxes of cereal.

82.SNACKS A candy warehouse sells large four-pound bags of M & M’s. There are approximately 180 peanut M & M’s per pound. How many peanut M & M’s are there in one bag?

Peanut

m m

m m m

m m

NET WT

4 LB

83.NUTRITION There are 17 grams of fat in one Krispy Kreme chocolate-iced, custard-ﬁlled donut. How many grams of fat are there in one dozen of those donuts?

84.JUICE It takes 13 oranges to make one can of orange juice. Find the number of oranges used to

make a case of 24 cans.

85.BIRDS How many times do a hummingbird’s wings beat each minute?

86.LEGAL FEES Average hourly rates for lead attorneys in New York are $775. If a lead attorney bills her client for 15 hours of legal work, what is the fee?

87.CHANGING UNITS There are 12 inches in 1 foot and 5,280 feet in 1 mile. How many inches are there in a mile?

88.FUEL ECONOMY Mileage ﬁgures for a 2009 Ford Mustang GT convertible are shown in the table.

a.For city driving, how far can it travel on a tank of gas?

b.For highway driving, how far can it travel on a tank of gas?

Fuel tank capacity

16 gal

Fuel economy (miles per gallon) 15 city/23 hwy

89.WORD COUNT Generally, the number of words on a page for a published novel is 250. What would be the expected word count for the 308-page children’s novel Harry Potter and the Philosopher’s Stone?

90.RENTALS Mia owns an apartment building with 18 units. Each unit generates a monthly income of $450. Find her total monthly income.

91.CONGRESSIONAL PAY The annual salary of a U.S. House of Representatives member is $169,300. What does it cost per year to pay the salaries of all 435 voting members of the House?

92.CRUDE OIL The United States uses 20,730,000 barrels of crude oil per day. One barrel contains 42 gallons of crude oil. How many gallons of crude oil does the United States use in one day?

93.WORD PROCESSING A student used the Insert Table options shown when typing a report. How many entries will the table hold?

	Document 1
.
.	File Edit View Insert Format Tools Data Window Help
.	File Edit View Insert Format Tools Data Window Help

Insert Table

Table size

Number of columns:		8
Number of rows:		9

94.BOARD GAMES A checkerboard consists of 8 rows, with 8 squares in each row. The squares alternate in color, red and black. How many squares are there on a checkerboard?

95.ROOM CAPACITY A college lecture hall has 17 rows of 33 seats each. A sign on the wall reads,

“Occupancy by more than 570 persons is prohibited.” If all of the seats are taken, and there is one instructor in the room, is the college breaking the rule?

96.ELEVATORS There are 14 people in an elevator with a capacity of 2,000 pounds. If the average weight of a person in the elevator is 150 pounds, is the elevator overloaded?

97.KOALAS In one 24-hour period, a koala sleeps 3 times as many hours as it is awake. If it is awake for 6 hours, how many hours does it sleep?

98.FROGS Bullfrogs can jump as far as ten times their body length. How far could an 8-inch-long bullfrog jump?

99.TRAVELING During the 2008 Olympics held in Beijing, China, the cost of some hotel rooms was 33 times greater than the normal charge of $42 per night. What was the cost of such a room during the Olympics?

100.ENERGY SAVINGS An ENERGY STAR light

bulb lasts eight times

longer than a standard Shutterstock.com 60-watt light bulb. If a

standard bulb normally 2009. lasts 11 months, how long Gill, from

will an ENERGY STAR Josecopyright license

bulb last? under

Image

Used

1.4 Multiplying Whole Numbers

101.PRESCRIPTIONS How many tablets should a pharmacist put in the container shown in the illustration?

R a m i r e z

Pharmacy

No. 2173

11/09

Take 2 tablets 3 times a day for 14 days

Expires: 11/10

102.HEART BEATS A normal pulse rate for a healthy adult, while resting, can range from 60 to 100 beats per minute.

a.How many beats is that in one day at the lower end of the range?

b.How many beats is that in one day at the upper end of the range?

103.WRAPPING PRESENTS When completely unrolled, a long sheet of wrapping paper has the dimensions shown. How many square feet of gift wrap

104.POSTER BOARDS A rectangular-shaped poster board has dimensions of 24 inches by 36 inches. Find its area.

105.WYOMING The state of Wyoming is approximately rectangular-shaped, with dimensions 360 miles long and 270 miles wide. Find its perimeter and its area.

106.COMPARING ROOMS Which has the greater area, a rectangular room that is 14 feet by

17 feet or a square room that is 16 feet on each side? Which has the greater perimeter?

WRITING

107.Explain the difference between 1 foot and 1 square foot.

108.When two numbers are multiplied, the result is 0. What conclusion can be drawn about the numbers?

REVIEW

109.Find the sum of 10,357, 9,809, and 476.

110.DISCOUNTS A radio, originally priced at $367, has been marked down to $179. By how many dollars was the radio discounted?

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