1. business and industrial

Find Percent of a Number Mentally
Why?
Then
You have already found
percents using the
percent
proportion. (Lesson 7-3)
Now
Compute mentally with
percents.
Estimate with percents.
Math Online
glencoe.com
Team
The table shows the final standing of the
first, second, and third place finishers in
a recent Women’s World Cup soccer
tournament.
Number of Wins
Germany
5
United States
4
Norway
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.
Extra Examples
Personal Tutor
0%
12.5%
25%
40%
50%
66 2 %
75%
87.5%
100%
Self-Check Quiz
0
1
8
1
4
2
5
1
2
2
3
3
4
7
8
1
Homework Help
Concept Summary
3
For Your
Percent-Fraction Equivalents
_
25% =$"
20% = _
1
4
1
5
1
10% = _
1
1
12_% = _
2
1
16_% = _
1
50% = _
2
40% = _
3
30% = _
3
1
37_% = _
1
1
33_% = _
3
75% = _
3
60% = _
7
70% = _
5
1
62_% = _
2
2
66_% = _
1
100% = _
4
80% = _
9
90% = _
1
7
87_% = _
5
1
83_% = _
EXAMPLE 1
Use a Fraction to Compute Mentally
5
2
4
5
5
1
10
10
10
10
2
2
2
2
8
8
8
8
3
3
3
3
6
3
3
6
Find the percent of each number mentally.
a. 75% of 24
3
75% of 24 = _
of 24
4
= 18
THINK
75% =
5
= 48
4
THINK
_3 of 24 is 18.
THINK
80% =
4
b. 80% of 60
4
80% of 60 = _
of 60
_3
THINK
_4
5
_4 of 60 is 48.
5
✓ Check Your Progress
1A. 40% of 50 20
1B. 30% of 70 21
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Lesson 7-4 Find Percent of a Number Mentally
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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
1% of 122 = 0.01 · 122 or 1.22
✓ Check Your Progress
2A. 10% of 42 4.2
2B. 1% of 264 2.64
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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.
Every year nearly
300 billion coupons are
distributed nationwide.
About 90% of these
coupons are distributed
in Sunday newspapers.
Source: CMS, Inc.
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
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Estimate With Percents You can estimate when an exact answer is not needed.
Problem-SolvingTip
Determine Reasonable
Answers Deciding
whether an answer is
reasonable is useful
when an exact answer
is not necessary.
4A.
9
≈ 45; _ × 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
EXAMPLE 4
Estimate Percent of a Number
Estimate.
a. 26% of 64
b.
_2 % of 891
3
1
26% is about 25% or _
.
_2 % = _2 × 1%. 1% of 900 is 9.
_1 of 64 is 16.
891 is almost 900.
4
4
So, 26% of 64 is about 16.
c. 39% of 81
3
3
2
2
% of 891 is about _
× 9 or 6.
So, _
3
3
d. 120% of 51
2
39% is about 40% or _
.
5
100% of 50 is 50.
81 is about 80.
20% of 50 is 10.
_2 of 80 is 32.
So, 120% of 51 is about
So, 39% of 81 is about 32.
50 + 10 or 60.
5
✓ Check Your Progress
4A. 92% of 50
4B. 63% of 205
4C. 75% of 84
4D. 130% of 91
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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. 5. $7.50; Sample
answer: $48.61 ≈
$50.00, 10% · 50
= 5 and 15% · 50
= 2.50; 5 + 2.50
= 7.50
✓ 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.
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✓ Check Your Understanding
Examples 1 and 2
pp. 351–352
Example 3
p. 352
Example 4
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
Estimate. 8–13. See margin.
8. 11% of 70
9. 53% of 20
11. 87% of 42
Example 5
p. 353
pp. 351–352
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
= Step-by-Step Solutions begin on page R11.
Extra Practice begins on page 810.
Practice and Problem Solving
Examples 1 and 2
10. 40% of 19
1
12. _% of 598
3
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
1
19. 33 _
% of 27 9
1
20. 12 _
% of 48 6
1
21. 8 _
% of 72 6
3
2
3
23. 10% of 125 12.524. 10% of 259 25.9 25. 1% of 30 0.3
1
22. 87 _
% of 32 28
2
26. 1% of 400 4
Lesson 7-4 Find Percent of a Number Mentally
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Example 3
p. 352
Example 4
p. 352
27. SALES A store is having a sale where everything is 15% off. If Jeremy wants
to buy items that originally cost $50, how much will he save? $7.50
Estimate. 28–39. See margin.
28. 16% of 20
1
32. _% of 507
2
3
36. _% of 801
4
Example 5
p. 353
29. 73% of 84
1
33. _% of 295
6
4
37. _% of 30
5
30. 46% of 88
31. 25% of 49
34. 148% of 30
35. 276% of 8
38. 117% of 50
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
Portable
Portable MP3
MP3 Ownership
Ownership
65
+
55
-6
4
45
-5
4
35
-4
4
25
-3
4
18
-2
4
45%
40%
35%
30%
25%
20%
15%
10%
5%
0%
12
-1
7
42. MUSIC The bar graph shows
the percent of each age group
that owns a portable MP3
player. Suppose there are 825
12–17 year olds in the
Louisville School District.
About how many of them are
likely to own a portable
digital music player?
about 320 students
43. TRAVEL On a family trip,
Jenna’s family drove
310 miles from Gainesville
to Ft. Lauderdale.
Percent
B
Age Group
a. Her dad drove 52% of the
Source: Edison Media Research
way. About how many
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 mi
$"
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
C
Use Higher-Order Thinking Skills
2
45. OPEN ENDED Suppose you want to find 66 _
% of a. List two values of a for
3
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.
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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
C $36
D $40
$"
49. Which fraction
is between 85% and 90%? G
5
F _
6
9
H _
10
7
G _
J
8
3
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.
Thank you, come again.
A $28
B $32
50. Lorena, Julian, and Cho completed a
group assignment that had 84 questions.
1
Lorena answered _
of the questions, Julian
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?
10
_
d. If she only has $35, does she have
enough for tax and tip? Explain.
a–d. See Chapter 7 Answer Appendix.
11
Spiral Review
52. ACTIVITIES According to a survey about family activities, 35% of people said
3
they enjoy playing games, while three-fifths enjoy watching movies, and _
8 3
3
enjoy sports. Which group is the largest (Lesson 7-3) movies; Sample answer: = 37.5% and = 60%.
5
8
Since 60% is greater than 37.5% and 35%, movies are the favorite activity.
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)
k
3
54. _ = _
15
35
3
18
55. _ = _
4
t
7
24
10
5
56. _ = _
m 4.2
8.4
57. GEOMETRY The area A of the triangle is 33.75 square inches. Use the
1
formula A = _
bh to find the height h of the triangle. (Lesson 5-1) 7.5 in.
2
h
9 in.
Skills Review
Solve each equation. Check your solution. (Lesson 4-4)
C07-033A-888515
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58. 5 = 30b _
59. 40n = 10 0.25
60. 20 = 100k 0.20
61. 34g = 1.7 0.05
62. 3.6 = 90a 0.04
63. 200j = 70 0.35
6
Lesson 7-4 Find Percent of a Number Mentally
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