penny

nickel

dime

quarter

half-dollar

dollar

410

90

120

36

4

8

NumberType of Coin

5-4

COINS Paloma saves money by

putting all her spare change in a

large jar. She emptied the jar and

made a table listing the types of

coins she had saved.

1. Seventy-five percent of the

dimes she collected were

minted after the year 2000.

How could you find 75% of 120 mentally?

2. Use mental math to find the number of dimes minted after the

year 2000.

3. If 25% of the dollars she collected were Sacagawea dollars, use

mental math to find the number of Sacagawea dollars she collected.

When you compute with common percents like 75% or 25%, it may be

easier to use the fraction form of the percent. This number line shows

some fraction-percent equivalents.

0 118

14

38

12

58

34

78

0% 12.5% 25% 37.5% 50% 62.5% 75% 87.5% 100%

Since some percents are used more frequently than others, it is helpful

to be familiar with the percent-fraction equivalencies shown below.

Use Fractions to Compute Mentally

1 Compute 20% of 45 mentally.

20% of 45 = 1 _ 5 · 45 or 9 Use the fraction form of 20%, which is 1 _

5 .

Finding Percents Mentally

268 Chapter 5 Percent

MAIN IDEACompute mentally with percents.

Math Online

glencoe.com• Extra Examples• Personal Tutor• Self-Check Quiz

Key ConceptPercent-Fraction Equivalents

25% = 1 _ 4 20% = 1 _

5 16 2 _

3 % = 1 _

6 12 1 _

2 % = 1 _

8 10% = 1 _

10

50% = 1 _ 2 40% = 2 _

5 33 1 _

3 % = 1 _

3 37 1 _

2 % = 3 _

8 30% = 3 _

10

75% = 3 _ 4 60% = 3 _

5 66 2 _

3 % = 2 _

3 62 1 _

2 % = 5 _

8 70% = 7 _

10

100% = 1 80% = 4 _ 5 83 1 _

3 % = 5 _

6 87 1 _

2 % = 7 _

8 90% = 9 _

10

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2 Compute 33 1 _ 3 % of 93 mentally.

33 1 _ 3 % of 93 = 1 _

3 · 93 or 31 Use the fraction form of 33 1 _

3 %, which is 1 _

3 .

Compute mentally.

a. 25% of 32 b. 12 1 _ 2 % of 160 c. 80% of 45

You can also use decimals to find percents mentally. Remember that

10% = 0.1 and 1% = 0.01.

Use Decimals to Compute Mentally

Compute mentally.

3 10% of 98 4 1% of 235

10% of 98 = 0.1 · 98 or 9.8 1% of 235 = 0.01 · 235 or 2.35

d. 10% of 65 e. 1% of 450 f. 3% of 22

5 SPORTS The Weston Middle School Cougars won 80% of their

baseball games this year. There were 35 games. How many games

did the Cougars win?

METHOD 1 Use a fraction.

80% of 35 = 4 _ 5 of 35 THINK 1 _

5 of 35 is 7. So, 4 _

5 of 35

is 4 · 7 or 28.80% of 35 is 28.

METHOD 2 Use a decimal.

80% of 35 = 0.8 of 35 THINK 0.1 of 35 is 3.5. So, 0.8 of 35 is 8 · 3.5 or 28.

80% of 35 is 28.

The Cougars won 28 baseball games.

g. TIPPING Alan and his brother ate lunch at the local café. They left a

tip that was 20% of the bill. If the bill was $15.50, how much did

Alan and his brother leave for the tip?

Multiplying by DecimalsMultiplying by DecimalsTo multiply by 0.1, move the decimal point one place to the left. To multiply by 0.01, move the decimal point two places to the left.

Lesson 5-4 Finding Percents Mentally 269

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Examples 1–4(pp. 268–269)

Compute mentally.

1. 50% of 120 2. 33 1_3 % of 60 3. 37 1_

2 % of 72

4. 1% of 52 5. 10% of 350 6. 2% of 630

Example 5(p. 269)

7. BOOKS An author receives a payment, or commission, equal to 25% of the

total sales of her book. Determine the amount of money she will receive if

the total sales are $48,000.

For Exercises

See Examples

8–1516–2324, 25

1–23–45

HOMEWORK HELPHELP Compute mentally.

8. 25% of 44 9. 50% of 62 10. 12 1 _ 2 % of 64 11. 16 2 _

3 % of 54

12. 40% of 35 13. 60% of 15 14. 66 2 _ 3 % of 120 15. 62 1 _

2 % of 160

16. 10% of 57 17. 10% of 125 18. 1% of 81 19. 1% of 28.3

20. 3% of 130 21. 7% of 210 22. 10% of 17.1 23. 10% of 10.2

24. HAIR A blonde or brunette has about 100,000 hairs on her head. However,

a redhead averages only 90% of this number. What is the average number

of hairs on the head of a redhead?

25. TRAVEL About 10% of travel trips in the United States include a visit to an

amusement park. If there were 920 million travel trips in the United States,

how many of those included a visit to an amusement park?

Replace each ● with <, >, or = to make a true statement.

26. 66 2 _ 3 % of 18 ● 60% of 15 27. 1% of 150 ● 10% of 15

28. MEASUREMENT The Amazon is the second longest river in the world with a

length of about 4,000 miles. If the longest river in the world, the Nile, is

about 104% of the length of the Amazon, find the length of the Nile River.

MONEY For Exercises 29 and 30, use the following information.

The graphic shows the results of a survey asking teens

about their allowances. Suppose 1,000 teens were

surveyed.

29. How many teens receive at most $20 weekly

allowance?

30. How many teens receive less than a $10 weekly

allowance?

31. FIND THE DATA Refer to the Data File on pages 16–19.

Choose some data and write a real-world problem

in which you could mentally compute a percent.

270 Chapter 5 Percent

See pages 681, 704.EXTRA PRACTICEPRACTICE

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38. TESTS Alicia got 41 out of 52 questions correct on a test. What was her percent correct? (Lesson 5-3)

Write each fraction as a percent. (Lesson 5-2)

39. 9 _ 20

45% 40. 7 _ 8 87.5% 41. 3 _

500 0.6% 42. 2 _

9 22.

− 2 %

43. MEASUREMENT A snail travels one mile in about 30 hours. At this rate, how far can a snail travel in 1 day? (Lesson 2-4)

PREREQUISITE SKILL Draw the next three figures in the pattern. (Lesson 2-8)

44.

H.O.T. Problems 32. CHALLENGE The sum of two whole numbers, x and y, is 90. Twenty percent of x is equal to 80% of y. Find the two numbers. Explain your reasoning.

33. OPEN ENDED Find two values of x for which you could mentally find 66 2 _ 3 %

of x. Explain your reasoning.

34. FIND THE ERROR Camille and Manuel are finding 10% of 95. Who is correct? Justify your choice.

Camille Manuel

10% of 95 = 9.510% of 95 = 0.95

35. MATHWRITING IN Explain how to find 75% of 40 mentally.

Lesson 5-4 Finding Percents Mentally 271

36. Allison, Raul, and Theo drove from Austin, Texas, to Los Angeles, California, a distance of 1,224 miles.

Allison drove 1 _ 3 of the total distance,

Raul drove 40%, and Theo drove the remainder. How many miles were driven by the person who drove the greatest distance?

A 330.5 C 489.6

B 408 D 734.4

37. Etu bought the items listed below. How much money did he save if each item was 20% off the regular price?

Item Regular Price ($)Shirt 19Ties 9Belt 8Shoes 29

F $52 H $24

G $36 J $13

Allison, Raul, and Theo drove from

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