226 Chapter 6 Percents

The Percent Proportion6.3

How can you use models to estimate

percent questions?

The statement “25% of 12 is 3” has three numbers. In real-life problems, any one of these numbers can be unknown.

Which number Question is missing? Type of Question

What is 25% of 12? 3 Find a part of a number.

3 is what percent of 12? 25% Find a percent.

3 is 25% of what? 12 Find the whole.

Work with a partner. Use a model to estimate the answer to each question.

a. What number is 50% of 30?

0 15 30

0% 50% 100%

So, from the model, is 50% of 30.

b. What number is 75% of 30? c. What number is 40% of 30?

d. What number is 6% of 30? e. What number is 65% of 30?

ACTIVITY: Estimating a Part11

Work with a partner. Use a model to estimate the answer to each question.

a. 15 is what percent of 75?

0 75

0% 100%20%

15

40%

30

60%

45

80%

60

So, from the model, 15 is of 75.

b. 5 is what percent of 20? c. 18 is what percent of 40?

d. 50 is what percent of 80? e. 75 is what percent of 50?

ACTIVITY: Estimating a Percent22COMMON CORE

Percent ProportionIn this lesson, you will● use the percent

proportion to fi nd parts, wholes, and percents.

Learning Standard7.RP.3

Section 6.3 The Percent Proportion 227

Work with a partner. Use a model to estimate the answer to each question.

a. 24 is 33 1

— 3

% of what number?

0 72

0% 100%

24 48

33 %13 66 %2

3

So, from the model, 24 is 33 1

— 3

% of .

b. 13 is 25% of what number? c. 110 is 20% of what number?

d. 75 is 75% of what number? e. 81 is 45% of what number?

Work with a partner. Use a ratio table to answer each question. Then compare your answer to the estimate you found using the model.

a. What number is 6% of 30? b. What number is 65% of 30?

Part 6

Whole 100 30

Part 65

Whole 100 30

c. 18 is what percent of 40? d. 81 is 45% of what number?

Part 18

Whole 40 100

Part 45 81

Whole 100

ACTIVITY: Estimating a Whole33

ACTIVITY: Using Ratio Tables44

5. IN YOUR OWN WORDS How can you use models to estimate percent questions? Give examples to support your answer.

6. Complete the proportion below using the given labels.

percent

100

whole

part

=

Use what you learned about estimating percent questions to complete Exercises 5–10 on page 230.

Use a ModelWhat quantities are given? How can you use the model to fi nd the unknown quantity?

Math Practice

1d1d

2c2c

1e1e

3e3e

228 Chapter 6 Percents

Lesson6.3

What percent of 15 is 12?

a

— w

= p —

100 Write the percent proportion.

12

— 15

= p —

100 Substitute 12 for a and 15 for w.

100 ⋅ 12

— 15

= 100 ⋅ p —

100 Multiplication Property of Equality

80 = p Simplify.

So, 80% of 15 is 12.

0

0% 100%20%

3

40%

6

60%

9

80%

12 15

EXAMPLE Finding a Percent11

What number is 36% of 50?

a

— w

= p —

100 Write the percent proportion.

a

— 50

= 36

— 100

Substitute 50 for w and 36 for p.

50 ⋅ a

— 50

= 50 ⋅ 36

— 100

Multiplication Property of Equality

a = 18 Simplify.

So, 18 is 36% of 50.

EXAMPLE Finding a Part22

Lesson Tutorials

The Percent Proportion

Words You can represent “a is p percent of w” with the proportion

a

— w

= p —

100

where a is part of the whole w, and p%, or p —

100 , is the percent.

Numbers 3 out of 4 is 75%.

3

— 4

= 75

— 100

whole

partpercent

Study TipIn percent problems, the word of is usually followed by the whole.

Section 6.3 The Percent Proportion 229

150% of what number is 24?

a

— w

= p —

100 Write the percent proportion.

24

— w

= 150

— 100

Substitute 24 for a and 150 for p.

24 ⋅ 100 = w ⋅ 150 Cross Products Property

2400 = 150w Multiply.

16 = w Divide each side by 150.

So, 150% of 16 is 24.

0

0% 150%50%

8

100%

16 24

Write and solve a proportion to answer the question.

1. What percent of 5 is 3? 2. 25 is what percent of 20?

3. What number is 80% of 60? 4. 10% of 40.5 is what number?

5. 0.1% of what number is 4? 6. 1

— 2

is 25% of what number?

EXAMPLE Finding a Whole33

Exercises 11 –18

The bar graph shows the strengths of tornadoes that occurred in Alabama in 2011. What percent of the tornadoes were EF1s?

The total number of tornadoes, 145, is the whole, and the number of EF1 tornadoes, 58, is the part.

a

— w

= p —

100 Write the percent proportion.

58

— 145

= p —

100 Substitute 58 for a and 145 for w.

100 ⋅ 58

— 145

= 100 ⋅ p —

100 Multiplication Property of Equality

40 = p Simplify.

So, 40% of the tornadoes were EF1s.

7. Twenty percent of the tornadoes occurred in central Alabama on April 27. How many tornadoes does this represent?

EXAMPLE Real-Life Application44

10

20

30

40

50

60

70

0EF0

36

EF1

58

EF2

29

EF3

13

EF4

7

EF5

2

Strength

Nu

mb

er o

f to

rnad

oes

2011 Alabama Tornadoes

Exercises6.3

230 Chapter 6 Percents

1. VOCABULARY Write the percent proportion in words.

2. WRITING Explain how to use a proportion to fi nd 30% of a number.

3. NUMBER SENSE Write and solve the percent

0

0% 100%20% 40% 60% 80%

40proportion represented by the model.

4. WHICH ONE DOESN’T BELONG? Which proportion does not belong with the other three? Explain your reasoning.

15

— w

= 50

— 100

12

— 15

= 40

— n

15

— 25

= p —

100

a

— 20

= 35

— 100

9+(-6)=3

3+(-3)=

4+(-9)=

9+(-1)=

Use a model to estimate the answer to the question. Use a ratio table to check your answer.

5. What number is 24% of 80? 6. 15 is what percent of 40?

7. 15 is 30% of what number? 8. What number is 120% of 70?

9. 20 is what percent of 52? 10. 48 is 75% of what number?

Write and solve a proportion to answer the question.

11. What percent of 25 is 12? 12. 14 is what percent of 56?

13. 25% of what number is 9? 14. 36 is 0.9% of what number?

15. 75% of 124 is what number? 16. 110% of 90 is what number?

17. What number is 0.4% of 40? 18. 72 is what percent of 45?

a —

w = p

— 100

a — 34

= 40 —

100

a = 13.6

✗ 19. ERROR ANALYSIS Describe and correct the error

in using the percent proportion to answer the question below.

“40% of what number is 34?”

20. FITNESS Of 140 seventh-grade students, 15% earn the Presidential Physical Fitness Award. How many students earn the award?

21. COMMISSION A salesperson receives a 3% commission on sales. The salesperson receives $180 in commission. What is the amount of sales?

Help with Homework

11

22

33

Section 6.3 The Percent Proportion 231

Evaluate the expression when a = −15 and b = −5. (Section 1.5)

32. a ÷ b 33. b + 14

— a

34. b 2

— a + 5

35. MULTIPLE CHOICE What is the solution of 9x = −1.8? (Section 3.4)

○A x = −5 ○B x = −0.2 ○C x = 0.2 ○D x = 5

Write and solve a proportion to answer the question.

22. 0.5 is what percent of 20? 23. 14.2 is 35.5% of what number?

24. 3

— 4

is 60% of what number? 25. What number is 25% of 7

— 8

?

26. HOMEWORK You are assigned 32 math exercises for homework. You complete 87.5% of these before dinner. How many do you have left to do after dinner?

27. HOURLY WAGE Your friend earns $10.50 per hour. This is 125% of her hourly wage last year. How much did your friend earn per hour last year?

28. CAMPSITE The bar graph shows the numbers of reserved campsites at a campground for one week. What percent of the reservations were for Friday or Saturday?

29. PROBLEM SOLVING A classmate displays the

0Greg Diego Amber Rashad Chloe

Candidate

Vo

tes

Class President Electionresults of a class president election in the bar graph shown.

a. What is missing from the bar graph?

b. What percent of the votes does the last-place candidate receive? Explain your reasoning.

c. There are 124 votes total. How many votes does Chloe receive?

30. REASONING 20% of a number is x. What is 100% of the number? Assume x > 0.

31. Answer each question. Assume x > 0.

a. What percent of 8x is 5x? b. What is 65% of 80x?

5

10

15

20

25

30

35

0Mon

5

Tue

3

Wed

4

Thu

7

Fri

26

Sat Sun

30

9

Day

Res

erva

tio

ns

Campground

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