C H A P T E R S 1 – 5 CUMULATIVE REVIEW

1.Write 5,764,502:

a.in words

b.in expanded notation [Section 1.1]

2.BASKETBALL RECORDS On December 13, 1983, the Detroit Pistons and the Denver Nuggets played in the highest-scoring game in NBA history. See the game summary below. [Section 1.2]

a.What was the final score?

b.Which team won?

14.Evaluate: 32 and ( 3)2 [Section 2.4]

15.Evaluate each expression, if possible. [Section 2.5]

3 3 [5( 6) (1 10)D

c.What was the total number of points scored in the game?

(Source: ESPN.com)

3.Subtract: 70,006 348 [Section 1.3]

4.Multiply: 504 729 [Section 1.4]

5.Divide: 37 743 [Section 1.5]

6.DISCOUNT LODGING A hotel is offering rooms that normally go for $189 per night for only $109 a night. How many dollars would a traveler save if he stays in such a room for one week? [Section 1.6]

7.List the factors of 30, from smallest to largest.

[Section 1.7]

8.Find the prime factorization of 360.

[Section 1.7]

9.Find the LCM and the GCF of 20 and 28.

[Section 1.8]

10.Evaluate: 81 9 C72 7(11 4)D [Section 1.9]

12.Evaluate: ( 12 6) ( 6 8) [Section 2.2]

13.GOLF Tiger Woods won the 100th U.S. Open in June of 2000 by the largest margin in the history of that tournament. If he shot 12 under par ( 12) and the second-place finisher, Miguel Angel Jimenez, shot 3 over par ( 3), what was Tiger’s margin of victory?

17.Estimate the value of the following expression by rounding each number to the nearest hundred.

[Section 2.6]

3,887 ( 5,806) 4,701

16

18. Simplify: 20 [Section 3.1]

19. Express 109 as an equivalent fraction with a denominator of 60. [Section 3.1]

20. GEOGRAPHY Earth has a surface area of about

197,000,000 square miles. Use the information in the circle graph below to determine the number of square miles of Earth’s surface covered by land. (Source: scienceclarified.com) [Section 3.2]

Land covers about

3

–– of the Earth’s surface 10

Water covers about

7

–– of the Earth’s surface 10

21.What is the formula for the area of a triangle?

[Section 3.2]

77

22.Divide: 8 8 [Section 3.3]

117

23.Subtract: 12 15 [Section 3.4]

195

24.Determine which fraction is larger: 15 or 4

[Section 3.4]

25.HARDWARE Find the length of the wood screw shown below. [Section 3.4]

5 Head: –– in.

32

5 Shank: –– in.

16

1 Thread: – in.

2

27.MOTORS What is the difference in horsepower (hp) between the two motors shown? [Section 3.6]

line. [Section 4.1]

−5 − 4 −3 −2 −1 0 1 2 3 4 5

31.Add: 20.04 2.4 [Section 4.2]

32.Subtract: 8.08 15.3 [Section 4.2]

33.Multiply: 2.5 100 [Section 4.3]

34.AQUARIUMS One gallon of water weighs 8.33 pounds. What is the weight of the water in an aquarium that holds 55 gallons of water?

40.Express the phrase “3 inches to 15 inches” as a ratio in simplest form. [Section 5.1]

41.BUILDING MATERIALS Which is the better buy:

a94-pound bag of cement for $4.48 or a 100-pound bag of cement for $4.80? [Section 5.1]

42.Determine whether the proportion 2533 1217 is true or false. [Section 5.2]

43.CAFFEINE There are 55 milligrams of caffeine in 12 ounces of Mountain Dew. How many milligrams of caffeine are there in a super-size 44-ounce cup

of Mountain Dew? Round to the nearest milligram.

[Section 5.2]

44.Solve the proportion: x3 357 [Section 5.2]

45.SURVIVAL GUIDE [Section 5.3]

a.A person can go without food for about 40 days. How many hours is this?

b.A person can go without water for about 3 days. How many minutes is that?

c.A person can go without breathing oxygen for about 8 minutes. How many seconds is that?

46.Convert 40 ounces to pounds. [Section 5.3]

47.Convert 2.4 meters to millimeters. [Section 5.4]

48.Convert 320 grams to kilograms. [Section 5.4]

49.a. Which holds more: a 2-liter bottle

or a 1-gallon bottle? [Section 5.5]

b.Which is longer: a meterstick or a yardstick?

50.BELTS A leather belt made in Mexico is 92 centimeters long. Express the length of the belt to the nearest inch. [Section 5.5]

Percent

from Campus to Careers

Loan Officer

Loan officers help people apply for loans. Commercial loan businesses, mortgage loan officers work with people who want buy a house or other real estate, and consumer loan

officers work with people who want to buy a boat, a car, or need a loan for college. Loan officers analyze the applicant’s financial history and often use banking formulas to determine the possibility of granting a loan.

In Problem 43 of Study Set 6.5, you will see how a credit union loan officer calculates the interest to be charged on a loan.

6

6.1Percents, Decimals, and Fractions

6.2Solving Percent Problems Using Percent Equations and Proportions

6.3Applications of Percent

6.4Estimation with Percent

6.5Interest

Chapter Summary and Review

Chapter Test Cumulative Review

Ariel Skelley/Getty Images

3Write percents as decimals.

4Write decimals as percents.

5Write fractions as percents.

We see percents everywhere, everyday. Stores use them to advertise discounts, manufacturers use them to describe the contents of their products, and banks use them to list interest rates for loans and savings accounts. Newspapers are full of information presented in percent form. In this section, we introduce percents and show how fractions, decimals, and percents are related.

The Double Flex CD, only from Cal Fed Savings

Self Check 1

BOARD GAMES A standard Scrabble game contains 100 tiles. There are 42 vowel tiles, 2 blank tiles, and the rest are consonant tiles.

a.What percent of the tiles are vowels?

b.What percent of the letter tiles are consonants?

Now Try Problem 13

Self Check 2

WATERMELONS An average watermelon is 92% water. Write this percent as a fraction in simplest form.

Now Try Problems 17 and 23

Self Check 3

UNIONS In 2002, 13.3% of the U.S. labor force belonged to a union. Write this percent as a fraction in simplest form.

Now Try Problems 27 and 31

Self Check 4

Write 8313% as a fraction in simplest form.

Now Try Problem 35

6623 66 2 100

100 32003 1001

200 1

3 100

1

2 100 1

3 100

1

23

The fraction bar indicates division.

Write 66 32 as a mixed number and then multiply by the reciprocal of 100.

Multiply the numerators.

Multiply the denominators.

To simplify the fraction, factor 200 as 2 100. Then remove the common factor of 100 from the numerator and denominator.

Self Check 5

a.Write 210% as a fraction in simplest form.

b.Write 0.54% as a fraction in simplest form.

Now Try Problems 39 and 43

Self Check 6

a.Write 16.43% as a decimal.

b.Write 2.06% as a decimal.

Now Try Problems 51 and 57

Success Tip When percents that are greater than 100% are written as fractions, the fractions are greater than 1. When percents that are less than 1% are written as fractions, the fractions are less than 1001 .

3 Write percents as decimals.

To write a percent as a decimal, recall that a percent can be written as a fraction with denominator 100 and that a denominator of 100 indicates division by 100.

For example, consider 14%, which means 14 parts per 100.

14 100 The fraction bar indicates division.

14.0 100 Write the whole number 14 in decimal notation by placing a decimal

point immediately to its right and entering a zero to the right of the decimal point.

We have found that 14% 0.14. This example suggests the following procedure.

Writing Percents as Decimals

To write a percent as a decimal, drop the % symbol and divide the given number by 100 by moving the decimal point 2 places to the left.

(Source: marketingcharts.com)

given number by 100 by

moving the decimal point 2 places to the left.

WHY Recall from Section 4.4 that to find the quotient of a decimal and 10, 100, 1,000, and so on, move the decimal point to the left the same number of places as there are zeros in the power of 10.

Solution

a.From the graph, we see that the percent market share for the American Idol website is 32.86%. To write this percent as a decimal, we proceed as follows.

32.86%, written as a decimal, is 0.3286.

b.From the graph, we see that the percent market share for the Deal or No Deal website is 4.52%. To write this percent as a decimal, we proceed as follows.

4.52%, written as a decimal, is 0.0452.

The population of the state of Oregon is approximately 114% of the population of the United States.Write this percent as a decimal. (Source: U.S. Census Bureau)

Strategy We will write the mixed number 114 in decimal notation.

WHY With 114 in mixed-number form, we cannot apply the rule for writing a percent as a decimal; there is no decimal point to move 2 places to the left.

Solution To change a percent to a decimal, we drop the percent symbol and divide by 100 by moving the decimal point 2 places to the left. In this case, however, there is no decimal point to move in 114 %. Since 114 1 14 , and since the decimal equivalent of 14 is 0.25, we can write 114 % in an equivalent form as 1.25%.

114 %, written as a decimal, is 0.0125.

EXAMPLE 8

Strategy We will drop the % symbol and divide each given number by 100 by moving the decimal point two places to the left.

WHY Recall that to find the quotient of a decimal and 100, we move the decimal point to the left the same number of places as there are zeros in 100.

Solution

a. 310% 310.0% Write the whole number 310 in decimal notation: 310 310.0.

310%, written as a decimal, is 3.1.

0.9%, written as a decimal, is 0.009.

Self Check 7

POPULATION The population of the state of Ohio is approximately 334 % of the population of the United States. Write this percent as a decimal. (Source: U.S. Census Bureau)

Now Try Problem 59

Self Check 8

a.Write 600% as a decimal.

b.Write 0.8% as a decimal.

Now Try Problems 63 and 67

Self Check 9

Write 0.5343 as a percent.

Now Try Problems 71 and 75

Self Check 10

Write 7 out of 8 as a percent.

Now Try Problem 79

4 Write decimals as percents.

To write a percent as a decimal, we drop the % symbol and move the decimal point 2 places to the left. To write a decimal as a percent, we do the opposite: we move the decimal point 2 places to the right and insert a % symbol.

Writing Decimals as Percents

To write a decimal as a percent, multiply the decimal by 100 by moving the decimal point 2 places to the right, and then insert a % symbol.

Geography Land areas make up 0.291 of Earth’s surface. Write this decimal as a percent.

Strategy We will multiply the decimal by 100 by moving the decimal point 2 places to the right, and then insert a % symbol.

WHY To write a decimal as a percent, we reverse the steps used to write a percent as a decimal.

Solution

0.291 0 29.1% Multiply 0.291 by 100 by moving the decimal point 2

places to the right, and then insert a % symbol.

29.1%

0.291, written as a percent, is 29.1%

5 Write fractions as percents.

We use a two-step process to write a fraction as a percent. First, we write the fraction as a decimal. Then we write that decimal as a percent.

Writing Fractions as Percents

To write a fraction as a percent:

1.Write the fraction as a decimal by dividing its numerator by its denominator.

2.Multiply the decimal by 100 by moving the decimal point 2 places to the right, and then insert a % symbol.

Television The highest-rated television show of all time was a special episode of M*A*S*H that aired February 28, 1983. Surveys found that three out of every five American households watched this show. Express the rating as a percent.

Strategy First, we will translate the phrase three out of every five to fraction form and write that fraction as a decimal. Then we will write that decimal as a percent.

0.6

5 3.0

3 0

0

Write a decimal point and one additional zero to the right of 3.

The remainder is 0.

3

5 0.6

0.6 0 60.%

60%

Write a placeholder 0 to the right of the 6 (shown in blue). Multiply 0.60 by 100 by moving the decimal point 2 places to the right, and then insert a % symbol.

60% of American households watched the special episode of M*A*S*H.

Write 134 as a percent.

Strategy We will write the fraction 134 as a decimal. Then we will write that decimal as a percent.

WHY A fraction-to-decimal-to-percent approach must be used to write a fraction as a percent.

Solution

Step 1 To write 134 as a decimal, we divide the numerator, 13, by the denominator, 4.

3.25

4 13.00 Write a decimal point and two additional zeros to the right of 3.

The result is a terminating decimal.

Step 2 To write 3.25 as a percent, we proceed as follows.

3.25 325 % Multiply 3.25 by 100 by moving the decimal point 2 places

to the right, and then insert a % symbol.

325%

The fraction 134 , written as a percent, is 325%.

Success Tip When fractions that are greater than 1 are written as percents, the percents are greater than 100%.

In Examples 10 and 11, the result of the division was a terminating decimal. Sometimes when we write a fraction as a decimal, the result of the division is a repeating decimal.

Self Check 11

Write 52 as a percent.

Now Try Problem 85

Self Check 12

Write 23 as a percent. Give the exact answer and an approximation to the nearest tenth of one percent.

Now Try Problem 91

In the following illustrations, each set of 100 square regions represents 100%. What percent is shaded?

For Problems 13–16, see Example 1.

13.THE INTERNET The following sentence appeared on a technology blog: “Ask Internet users what they want from their service and 99 times out of 100 the answer will be the same: more speed.” According to the blog, what percent of the time do Internet users give that answer?

14.BASKETBALL RECORDS In 1962, Wilt Chamberlain of the Philadelphia Warriors scored a total of 100 points in an NBA game. If twenty-eight of his points came from made free throws, what percent of his point total came from free throws?

15.QUILTS A quilt is made from 100 squares of colored cloth.

a.If fifteen of the squares are blue, what percent of the squares in the quilt are blue?

b.What percent of the squares are not blue?

16.DIVISIBILITY Of the natural numbers from 1 through 100, only fourteen of them are divisible by 7.

a.What percent of the numbers are divisible by 7?

b.What percent of the numbers are not divisible by 7?

510 Chapter 6 Percent

Write each percent as a fraction.Simplify,if possible.See Example 2.

Write each percent as a fraction.Simplify,if possible.See Example 3.

Write each percent as a fraction.Simplify,if possible.See Example 4.

Write each percent as a fraction.Simplify,if possible.See Example 5.

Write each percent as a decimal. See Objective 3.

Write each percent as a decimal. See Example 6.

Write each percent as a decimal. See Example 7.

Write each percent as a decimal. See Example 8.

Write each decimal or whole number as a percent.See Example 9.

Write each fraction as a percent. See Example 10.

Write each fraction as a percent. See Example 11.

Write each fraction as a percent. Give the exact answer and an approximation to the nearest tenth of one percent.See Example 12.

TRY IT YOURSELF

Complete the table. Give an exact answer and an approximation to the nearest tenth of one percent when necessary. Round decimals to the nearest hundredth when necessary.

APPLICATIONS

101.THE RED CROSS A fact sheet released by the American Red Cross in 2008 stated, “An average of 91 cents of every dollar donated to the Red Cross is spent on services and programs.” What percent of the money donated to the Red Cross went to services and programs?

102.SAVING MONEY According to an article on the CNN website, in 1970 Americans saved 14 cents out of every dollar earned. (Source: CNN.com/living, May 21, 2009)

a.Express the amount saved for every dollar earned as a fraction in simplest form.

b.Write your answer to part a as a percent.

103.REGIONS OF THE COUNTRY The continental United States is divided into seven regions as shown below.

a.What percent of the 50 states are in the Rocky Mountain region?

b.What percent of the 50 states are in the Midwestern region?

c.What percent of the 50 states are not located in any of the seven regions shown here?

Midwestern

Pacific

Coast

States

104.ROAD SIGNS Sometimes, signs like that shown below are posted to warn truckers when they are approaching a steep grade on the highway.

105.INTEREST RATES Write each interest rate for the following accounts as a decimal.

a.Home loan: 7.75%

b.Savings account: 5%

c.Credit card: 14.25%

106.DRUNK DRIVING In most states, it is illegal to drive with a blood alcohol concentration of 0.08% or higher.

a.Write this percent as a fraction. Do not simplify.

b.Use your answer to part a to fill in the blanks: A

blood alcohol concentration of 0.08% means parts alcohol to parts blood.

107.HUMAN SKIN The illustration below shows what percent of the total skin area that each section of the body covers. Find the missing percent for the torso, and then complete the bar graph. (Source: Burn Center at Sherman Oaks Hospital,American Medical Assn. Encyclopedia of Medicine)

108.RAP MUSIC The table below shows what percent rap/hip-hop music sales were of total U.S. dollar sales of recorded music for the years 2001–2007. Use the data to construct a line graph.

2001 2002 2003 2004 2005 2006 2007

Year

Source: Recording Industry Association of America

109.THE U.N. SECURITY COUNCIL The United Nations has 192 members. The United States, Russia, the United Kingdom, France, and China, along with ten other nations, make up the Security Council. (Source: The World Almanac and Book of Facts, 2009)

a.What fraction of the members of the United Nations belong to the Security Council? Write your answer in simplest form.

b.Write your answer to part a as a decimal. (Hint: Divide to six decimal places. The result is a terminating decimal.)

c.Write your answer to part b as a percent.

116.TAXES In August of 2008, Springfield, Missouri, voters approved a one-eighth of one percent sales tax to fund transportation projects in the city.

a.Write the percent as a decimal.

b.Write the percent as a fraction.

117.BIRTHDAYS If the day of your birthday represents 3651 of a year, what percent of the year is it? Round to the nearest hundredth of a percent.

118.POPULATION As a fraction, each resident of the

1

United States represents approximately 305,000,000 of the U.S. population. Express this as a percent.

Round to one nonzero digit.

WRITING

119.If you were writing advertising, which form do you

think would attract more customers: “25% off” or “14 off”? Explain your reasoning.

120.Many coaches ask their players to give a 110% effort during practices and games. What do you think this means? Is it possible?

121.Explain how an amusement park could have an attendance that is 103% of capacity.

122.WON-LOST RECORDS In sports, when a team wins as many games as it loses, it is said to be playing “500 ball.” Suppose in its first 40 games, a team wins 20 games and loses 20 games. Use the concepts in this section to explain why such a record could be called “500 ball.”

REVIEW

123.The width of a rectangle is 6.5 centimeters and its length is 10.5 centimeters.

a.Find its perimeter.

b.Find its area.