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
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.
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.
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.
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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