Find Percent of a Number Mentally - Glencoe

Then

You have already found percents using the percent proportion. (Lesson 7-3)

Now

Compute mentally with percents. Estimate with percents.

Math Online

Extra Examples Personal Tutor Self-Check Quiz Homework Help

Find Percent of a Number Mentally

Why?

The table shows the final standing of the first, second, and third place finishers in a recent Women's World Cup soccer tournament.

Team Germany United States Norway

Number of Wins 5 4 3

_ a. If the team from Norway won 50% of their games, use mental math to find the total number of games they played. 3 ? 1 = 6 games 2 b. If the team from Germany scored 2 goals in 40% of their winning games,

_ use mental math to find the number of winning games in which they scored

2 goals. 2 ? 5 = 2 games

5

Find Percent of a Number Mentally When you compute with common percents

like 40% or 50%, it may be easier to use the fraction form of the percent. The number line shows some common percent-fraction equivalents.

0%

12.5% 25%

40%

50%

66

2 3

%

75%

87.5% 100%

0

1

1

2

1

2

3

7

1

8

4

5

2

3

4

8

Concept Summary

Percent-Fraction Equivalents

For Your

25% =$_142"0%=_15

50%

=

_ 1

2

40%

=

_ 2

5

75%

=

_ 3

4

60%

=

_ 3

5

100%

=

_ 1

1

80%

=

_ 4

5

10%

=

_ 1

10

30%

=

_ 3

10

70%

=

_ 7

10

90%

=

_ 9

10

12_12 %

=

_ 1

8

37_12 %

=

_ 3

8

62_12 %

=

_ 5

8

87_12 %

=

_ 7

8

16_23 %

=

_ 1

6

33_13 %

=

_ 1

3

66_23 %

=

_ 2

3

83_13 %

=

_ 5

6

EXAMPLE 1 Use a Fraction to Compute Mentally

Find the percent of each number mentally.

a. 75% of 24

75%

of

24

=

_ 3

4

of

24

= 18

b. 80% of 60

80%

of

60

=

_ 4

5

of

60

= 48

Check Your Progress

THINK THINK

_ 75%

=

3 4

_ 3

4

of

24

is

18.

THINK THINK

_ 80%

=

4 5

_ 4

5

of

60

is

48.

1A. 40% of 50 20

1B. 30% of 70 21

Personal Tutor

Lesson 7-4 Find Percent of a Number Mentally 351

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EXAMPLE 2 Use Decimals to Compute Mentally

Compute mentally.

a. 10% of 76

b. 1% of 122

10% of 76 = 0.1 ? 76 or 7.6

Check Your Progress

2A. 10% of 42 4.2

1% of 122 = 0.01 ? 122 or 1.22

2B. 1% of 264 2.64

Personal Tutor

Every year nearly 300 billion coupons are distributed nationwide. About 90% of these coupons are distributed in Sunday newspapers.

Source: CMS, Inc.

EXAMPLE 3 Compute Mentally

SALES Hannah is shopping for school clothes. She has a coupon that will give her 20% off her entire purchase. If the items she buys cost $110 originally, how much will she save with her coupon?

You need to find 20% of the total cost. First, find 10% of 110.

10% of 110 = 0.1 ? 11.0

Move the decimal point one place to the left.

= 11

20% is the same as 2 ? 10%.

2 ? 10% = 2 ? 11 or 22

Replace 10% with 11.

So, Hannah will save $22 on her purchase.

Check Your Progress

3. SALES A television that costs $750 is on sale for 15% off. What is the total discount on the television? $112.50

Personal Tutor

Estimate With Percents You can estimate when an exact answer is not needed.

Problem-SolvingTip

EXAMPLE 4 Estimate Percent of a Number

Determine Reasonable Answers Deciding whether an answer is reasonable is useful when an exact answer is not necessary.

_ 4A. 45; 9 ? 50 or 45 10

4B. 126; 1% of 205 is about 2, 63% of 205 is about 63

_ ? 2 or 126

4C. 63; 3 ? 84 or 63

4

4D. 117; 100% of 90 = 90; 30% of 90 is 27, 90 + 27 = 117

Estimate.

a. 26% of 64

26%

_ 1

4

of

is about 64 is 16.

25%

or

_14 .

So, 26% of 64 is about 16.

c. 39% of 81

39% is about 40% or _25.

81 is about 80.

_ 2

5

of

80

is

32.

So, 39% of 81 is about 32.

Check Your Progress

4A. 92% of 50 4B. 63% of 205

_ b.

2 3

%

of

891

_23 %

=

_ 2

3

?

1%.

1%

of

900

is

9.

891 is almost 900.

So,

_23 %

of

891

is

about

_ 2

3

?

9

or

6.

d. 120% of 51

100% of 50 is 50.

20% of 50 is 10.

So, 120% of 51 is about

50 + 10 or 60.

4C. 75% of 84

4D. 130% of 91

Personal Tutor

352 Chapter 7 Percent

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5. $7.50; Sample answer: $48.61 $50.00, 10% ? 50 = 5 and 15% ? 50 = 2.50; 5 + 2.50 = 7.50

EXAMPLE 5 Estimate Percent of a Number

PIZZA Mr. Williams ordered 4 pizzas for a birthday party. The cost of the pizzas was $57.96. He wants to tip the delivery person about 15%. What is a reasonable amount for the tip?

Understand You need to find the tip for the delivery person. You know the cost of the pizzas.

Plan Estimate the price of the pizzas. Find 15% of the estimated price.

Solve $57.96 is about $60, and 15% = 10% + 5%.

10% of $60 is $6.00. Move the decimal point 1 place to the left.

5% of $60 is $3.00

5% is one half of 10%.

So, 15% is about $6.00 + $3.00 or $9.00.

A reasonable amount for the tip is $9.

Check 10% of $58 is $5.80 and 20% of $58 is $11.60. Since $5.80 < $9 < $11.60, the answer is reasonable.

Check Your Progress

5. RESTAURANT Haley went to dinner with her friends. Their bill was $48.61. They want to leave their server a 15% tip. What would be a reasonable amount for the tip? Explain your reasoning.

Personal Tutor

Check Your Understanding

Examples 1 and 2

pp. 351?352

Example 3

p. 352

Find the percent of each number mentally.

1 75% of 16 12

2. 25% of 32 8

3. 10% of 37 3.7

4. 10% of 115 11.5

5. 1% of 72 0.72

6. 1% of 231 2.31

7. HOMEWORK Jasmine has finished 30% of the exercises on her homework. If there are 40 exercises in all, how many has Jasmine completed? 12 exercises

Example 4

p. 352

Example 5

p. 353

Estimate. 8?13. See margin.

8. 11% of 70

9. 53% of 20

10. 40% of 19

11. 87% of 42

12. _13% of 598

13. 110% of 39

14. SPORTS Last basketball season, Carlos made 38% of the baskets he

attempted. At this rate, about how many baskets will he make if he

attempts 30 baskets? 12 baskets

Practice and Problem Solving

= Step-by-Step Solutions begin on page R11. Extra Practice begins on page 810.

Examples 1 and 2

pp. 351?352

Find the percent of each number mentally.

15. 40% of 80 32 16. 20% of 50 10 17. 25% of 280 70 18. 75% of 96 72

19. 33 _13% of 27 9 20. 12 _12% of 48 6 21. 8 _13% of 72 6

23. 10% of 125 12.524. 10% of 259 25.9 25. 1% of 30 0.3

22. 87 _12% of 32 28

26. 1% of 400 4

Lesson 7-4 Find Percent of a Number Mentally 353

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Example 3 27. SALES A store is having a sale where everything is 15% off. If Jeremy wants

p. 352

to buy items that originally cost $50, how much will he save? $7.50

Example 4

p. 352

Example 5

p. 353

Estimate. 28?39. See margin.

28. 16% of 20

32. _12% of 507 36. _34% of 801

29. 73% of 84

33. _16% of 295 37. _45% of 30

30. 46% of 88 34. 148% of 30

38. 117% of 50

31. 25% of 49 35. 276% of 8

39. 194% of 15

40. MANICURES The total cost for Soledad's manicure was $32.99. She wants to give the manicurist a 20% tip. What would be a reasonable amount for the tip? $6

41 INTERNET In a national survey of 6700 teens, 81% of teens between the ages

_ of 12 and 17 said they use the Internet to e-mail friends or relatives. About

how many teens is this? Sample answer: 4 ? 6700 or 5360 teens

5

B 42. MUSIC The bar graph shows the percent of each age group

PPoorrttaabbllee MMPP33 OOwwnneerrsshhiipp

that owns a portable MP3

45%

player. Suppose there are 825

40%

12?17 year olds in the

35%

Louisville School District.

30%

About how many of them are

25%

Percent

likely to own a portable

20%

digital music player?

15%

about 320 students

10%

43. TRAVEL On a family trip, Jenna's family drove 310 miles from Gainesville to Ft. Lauderdale.

5%

0% 12-17 18-24 25-34 35-44 45-54 55-64 65+ Age Group

a. Her dad drove 52% of the way. About how many

Source: Edison Media Research

miles did he drive? Sample answer: 155 mi

b. Jenna's mom drove 58% of the distance her dad drove. About how far did

she drive? Sample answer: 90 m$i"

c. Her older brother drove the remaining miles. About how many miles did he drive? Sample answer: 65 mi

44. ARTS About 41% of twelfth graders participated in school performing arts last year. A high school had 1800 students, one-fourth of which were twelfth graders. About how many twelfth graders participated in school performing arts? about 180 twelfth graders

H.O.T. Problems

Use Higher-Order Thinking Skills

C 45. OPEN ENDED Suppose you want to find 66 _23% of a. List two values of a for

which you could do the computation mentally. Explain your reasoning. 45?47. See Chapter 7 Answer Appendix.

46. CHALLENGE Find two numbers, x and y, such that 10% of x is the same as

40% of y. Explain your reasoning.

47. WRITING IN MATH Describe two different ways you could find 20% of 60 mentally.

354 Chapter 7 Percent

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Standardized Test Practice

48. Jerome bought the items listed. If he saved 20% on each item, what is the best estimate of how much he saved? A

RECEIPT

Qty. Item

Amount

1 Network Cable $50.00

1 CD 10-pack $12.00

1 Mouse

$24.00

1 Memory

$55.00

Thank you, come again.

A $28

C $36

B $32

D $40

49. Which fr$actionisb"etween85% and 90%? G

F

_ 5

6

H

_ 9

10

G

_ 7

8

J

_10

11

50. Lorena, Julian, and Cho completed a

group assignment that had 84 questions.

Lorena

answered

_ 1

3

of

the

questions,

Julian

answered 25% of the questions, and Cho

answered the rest. How many questions

were answered by the person who answered

the greatest number of questions? D

A 18 B 21

C 28 D 35

51. EXTENDED RESPONSE The price of Jamila's haircut is $28. There is also a 7% tax added to the bill and Jamila wants to tip the stylist 15% of the total bill. Justify each solution.

a. About how much is the tax on the bill?

b. Find the approximate cost including tax.

c. About how much of a tip will Jamila give the stylist?

d. If she only has $35, does she have enough for tax and tip? Explain. a?d. See Chapter 7 Answer Appendix.

Spiral Review

52. ACTIVITIES According to a survey about family activities, 35% of people said

_ _ they

enjoy

playing

games,

while

three-fifths

enjoy

watching

movies,

and

_ 3

8

enjoy sports. Which group is the largest (Lesson 7-3) movies; Sample answer:

Since 60% is greater than 37.5% and 35%, movies are the favorite activity.

3 8

=

37.5%

and

3 5

=

60%.

_ 53. GEOGRAPHY The Arctic Ocean contains 3.7% of the world's water. What fraction is this? (Lesson 7-2) 37 1000

ALGEBRA Solve each proportion. (Lesson 6-5)

54.

_ k

35

=

_ 3

7

15

55.

_ 3

t

=

_18

24

4

56.

_10

8.4

=

_ 5

m

4.2

57. GEOMETRY The area A of the triangle is 33.75 square inches. Use the

formula

A

=

_ 1

2

bh

to

find

the

height

h

of

the

triangle.

(Lesson 5-1)

7.5 in.

h

9 in.

Skills Review

_ Solve each equation. Check your solution. (Lesson 4-4)

58. 5 = 30b 1

59. 40n = 10 0.25

6

61. 34g = 1.7 0.05

62. 3.6 = 90a 0.04

C07-033A-888515 60. 20 = 100k 0.20 63. 200j = 70 0.35

Lesson 7-4 Find Percent of a Number Mentally 355

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