Transcript Holt CA Course 1 6-4

6-4 Percent of a Number
California
Standards
NS1.4 Calculate given percentages
of quantities and solve problems involving
discounts at sales, interest earned, and tips.
Also covered:
NS2.4
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6-4 Percent of a Number
The human body is made up mostly of water. In
fact, about 67% of a person’s total (100%) body
weight is water. If Cameron weighs 90 pounds,
about how much of his weight is water?
Recall that a percent is a part of 100. Since you
want to know the part of Cameron’s body that is
water, you can set up and solve a proportion to
find the answer.
Part
Whole
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n
67
=
100 90
Part
Whole
6-4 Percent of a Number
Additional Example 1: Using Proportions to Find
Percents of Numbers
Find the percent of each number.
A. 30% of 50
30 = n
100
50
30 · 50 = 100 · n
Write a proportion.
Set the cross products equal.
1,500 = 100n
Multiply.
1,500 = 100n
100
100
Divide each side by 100.
15 = n
30% of 50 is 15.
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6-4 Percent of a Number
Helpful Hint
When solving a problem with a percent
greater than 100%, the part will be
greater than the whole.
Holt CA Course 1
6-4 Percent of a Number
Additional Example 1: Using Proportions to Find
Percents of Numbers
Find the percent of each number.
B. 200% of 24
200 = n
Write a proportion.
100
24
200 · 24 = 100 · n Set the cross products equal.
4,800 = 100n
4,800 = 100n
100
100
48 = n
Multiply.
Divide each side by 100.
200% of 24 is 48.
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6-4 Percent of a Number
Check It Out! Example 1
Find the percent of each number.
A. 40% of 40
40 = n
100
40
40 · 40 = 100 · n
Write a proportion.
Set the cross products equal.
1,600 = 100n
Multiply.
1,600 = 100n
100
100
16 = n
Divide each side by 100.
40% of 40 is 16.
Holt CA Course 1
6-4 Percent of a Number
Check It Out! Example 1
Find the percent of each number.
B. 150% of 64
150 = n
Write a proportion.
100
64
150 · 64 = 100 · n Set the cross products equal.
9,600 = 100n
9,600 = 100n
100
100
96 = n
Multiply.
Divide each side by 100.
150% of 64 is 96.
Holt CA Course 1
6-4 Percent of a Number
In addition to using proportions, you can
find a percent of a number by using
decimal equivalents.
Holt CA Course 1
6-4 Percent of a Number
Additional Example 2: Using Decimal Equivalents
to Find Percents of Numbers
Find the percent of the number. Check
whether your answer is reasonable.
A. 9% of 80
9% of 80 = 0.09 · 80 Write the percent as a
decimal and multiply.
= 7.2
Check
Since 10% of 80 = 8, a reasonable answer for
9% of 80 is 7.2.
0
9%
40%
20%
20
0
7.2
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60%
40
80%
60
100%
80
6-4 Percent of a Number
Additional Example 2: Using Decimal Equivalents
to Find Percents of Numbers
Find the percent of the number. Estimate
to check whether your answer is reasonable.
B. 3% of 12
3% of 12 = 0.03 · 12
= 0.36
Write the percent as a
decimal and multiply.
Check
5% · 12 = 0.6, so 3% of 12 is a little less than
0.6. Thus 0.36 is a reasonable answer.
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6-4 Percent of a Number
Check It Out! Example 2
Find the percent of the number. Check whether
your answer is reasonable.
A. 21% of 40
21% of 40 = 0.21 · 40
= 8.4
Write the percent as a
decimal and multiply.
Check
Since 20% of 40 = 8, a reasonable answer for
21% of 40 is 8.4.
21%
0
20%
10
0
8.4
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40%
60%
20
80%
30
100%
40
6-4 Percent of a Number
Check It Out! Example 2
Find the percent of the number. Estimate
to check whether your answer is reasonable.
B. 6% of 18
6% of 18 = 0.06 · 18
= 1.08
Write the percent as a
decimal and multiply.
Check
5% · 20 = 1, so 6% of 18 is close to 1. Thus
1.08 is a reasonable answer.
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6-4 Percent of a Number
Additional Example 3: Geography Application
The estimated world population in 2001 was 6,157
million. About 40% of the people were 19 or
younger. What was the approximate number of
people 19 or younger, to the nearest million?
Find 40% of 6,157 million.
0.40 · 6,157
= 2,462.8
≈ 2,463
Write the percent as a decimal.
Multiply.
Round to the nearest whole
number.
The number of people 19 or younger was about
2,463 million.
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6-4 Percent of a Number
Check It Out! Example 3
The estimated world population in 2001 was 6,157
million. About 60% of the people were above 19
years of age. What was the approximate number
of people 19 or older, to the nearest million?
Find 60% of 6,157 million.
0.60 · 6,157
Write the percent as a decimal.
= 3,694.2
Multiply.
≈ 3,694
Round to the nearest whole
number.
The number of people 19 or older was about
3,694 million.
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