7-7 percent of a number learn to find the percent of a number

7-7 Percent of a Number

Learn to find the 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 67 = n Part100 90Whole Whole


Find the percent of each number.

Additional Example 1A: Using Proportions to Find Percents of Numbers

30% of 5030

100= n

5030 · 50 = 100 · n

1,500 = 100n

1,500 100 100

= 100n

15 = n

30% of 50 is 15.

Write a proportion.

Set the cross products equal.

Multiply.

Divide each side by 100 to isolatethe variable.


When solving a problem with a percent greater than 100%, the part will be greater than the whole.

Helpful Hint


Additional Example 1B: Using Proportions to Find Percents of Numbers


200% of 24200100

= n24

200 · 24 = 100 · n

4,800 = 100n

4,800 100 100

= 100n

48 = n

200% of 24 is 48.

Write a proportion.


Multiply.




Check It Out: Example 1A

40% of 4040

100= n

4040 · 40 = 100 · n

1,600 = 100n

1,600 100 100

= 100n

16 = n

40% of 40 is 16.

Write a proportion.


Multiply.



Check It Out: Example 1B


150% of 64150100

= n64

150 · 64 = 100 · n

9,600 = 100n

9,600 100 100

= 100n

96 = n

150% of 64 is 96.

Write a proportion.


Multiply.



In addition to using proportions, you can find the percent of a number by using decimal equivalents.


Find the percent of the number. Check whether your answer is reasonable.

Additional Example 2A: Using Decimal Equivalents to Find Percents of Numbers

9% of 80

9% of 80 = 0.09 · 80

= 7.2Model

Since 10% of 80 = 8, a reasonable answer for 9% of 80 is 7.2.

Write the percent as a decimal and multiply.

0 20% 40% 60% 80% 100%

0 60 8020 40

9%

7.2


Additional Example 2B: Using Decimal Equivalents to Find Percents of Numbers

Find the percent of the number. Estimateto check whether your answer is reasonable.

3% of 12

3% of 12 = 0.03 · 12

= 0.36

Estimate

5% of 12 = 0.6, so 3% of 12 is a little less than 0.6. Thus 0.36 is a reasonable answer.



Find the percent of the number. Check whether your answer is reasonable.

Check It Out: Example 2A

21% of 40

21% of 40 = 0.21 · 40

= 8.4Model

Since 20% of 40 = 8, a reasonable answer for 21% of 40 is 8.4.


0 20% 40% 60% 80% 100%

0 30 4010 20

21%

8.4


Check It Out: Example 2B

Find the percent of the number. Estimateto check whether your answer is reasonable.

6% of 18

6% of 18 = 0.06 · 18

= 1.08

Estimate

5% of 20 = 1, so 6% of 18 is close to 1. Thus 1.08 is a reasonable answer.



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

The number of people 19 or younger was about 2,463 million.

Write the percent as a decimal.

Multiply.


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

3,694.2

The number of people 19 or older was about 3,694 million.

Write the percent as a decimal.

Multiply.

7-7 percent of a number learn to find the percent of a number

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