PERCENTS

A percent is a ratio that compares a number to 100.

For example,

15%  =  15/100

To find the fraction equivalent of a percent, write the percent as a ratio with a denominator of 100 and simplify. 

25%  =  25/100  =  1/4

75%  =  75/100  =  3/4

To find the fraction equivalent of a percent, write the percent as a ratio with a denominator of 100 and simplify.

25%  =  25/100  =  0.25

60%  =  60/100  =  0.6

The greatest percent shown in the table is 100%, or 1. But percents can be greater than 100%. For example,

120%  =  120/100  =  1.2

You can also find percents that are less than 1%. For example,

0.5%  =  0.5/100  =  0.005

You can use the following percent proportion to find unknown values. 

part/whole  =  percent/100

Finding the Part

Example 1 : 

Find 50% of 20.

Solution : 

Use the percent proportion.

part/whole  =  percent/100

Let x represent the part.

x/20  =  50/100

Use Cross Products Property. 

x(100)  =  20(50)

100x  =  1000

Because x is multiplied by 100, divide each side by 100 to undo the multiplication.

100x/100  =  1000/100

x  =  10

50% of 20 is 10.

Example 2 : 

Find 120% of 60.

Solution : 

Use an equation.

Write an equation. Let x represent the part.

x  =  120% of 60

x  =  1.2(60)

x  =  72

120% of 60 is 72.

Finding the Percent

Example 3 : 

What percent of 80 is 20?

Solution : 

Use the percent proportion.

part/whole  =  percent/100

Let x represent the percent.

20/80  =  x/100

Use Cross Products Property. 

20(100)  =  80(x)

2000  =  80x

Because x is multiplied by 80, divide each side by 80 to undo the multiplication.

2000/80  =  80x/80

25  =  x

20 is 25% of 80.

Example 4 : 

88 is what % of 80?

Solution : 

Use an equation.

Write an equation. Let x represent the percent.

88  =  x ⋅ 80

88  =  80x

Because x is multiplied by 80, divide each side by 80 to undo the multiplication.

88/80  =  80x/80

1.1  =  x

The answer is a decimal. To write the decimal as a percent, multiply by 100.

1.1 ⋅ 100  =  x

110  =  x

88 is 110% of 80.

This answer is reasonable; 88 is more than 100% of 80.

Finding the Whole

Example 5 : 

30% of what number is 21?

Solution : 

Use the percent proportion.

part/whole  =  percent/100

Let x represent the whole.

21/x  =  30/100

Use Cross Products Property. 

21(100)  =  30(x)

2100  =  30x

Because x is multiplied by 30, divide each side by 30 to undo the multiplication.

2100/30  =  30x/30

70  =  x

30% of 70 is 21.

Example 6 : 

50 is 0.4% of what number?

Solution : 

Use an equation.

Write an equation. Let x represent the whole.

50  =  0.4% of x

Write the percent as a decimal.

50  =  0.004x

Because x is multiplied by 0.004, divide each side by 0.004 to undo the multiplication.

50/0.004  =  0.004x/0.004

12500  =  x

50 is 0.4% of 12500.

Career Application

Example 7 : 

Jewelers use the karat system to determine the amount of pure gold in jewelry. Pure gold is 24 karat, meaning the item is 100% gold. A 14.4-karat gold ring contains 14.4 parts gold and 9.6 parts other metal. What percent of the ring is gold? Round your answer to the nearest percent.

Solution : 

Use the percent proportion.

part/whole  =  percent/100

Let x represent the percent.

14.4/24  =  x/100

Use Cross Products Property. 

14.4(100)  =  24(x)

1440  =  24x

Because x is multiplied by 24, divide each side by 24 to undo the multiplication.

1440/24  =  24x/24

60  =  x

A 14.4-karat gold ring is 60% gold.

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