Calculating percentage

An SAT Math micro-topic under Percentages (Problem solving and data analysis). Free to read — no account needed.

A percent is just a fraction out of

100

. So

x\%

means

\frac{x}{100}

. To find

x\%

of a number, multiply that number by

\frac{x}{100}

.
For example,

20\%

150

\frac{20}{100} \times 150 = 30

To answer 'A is what percent of B', divide

A

B

and multiply by

100

.
So

30

out of

150

\frac{30}{150} \times 100 = 20\%

A percentage change compares a new value to the old one using the formula

\frac{\text{final} - \text{initial}}{\text{initial}} \times 100

.
A positive answer is an increase and a negative answer is a decrease.

For instance, a price rising from

40

50

is a change of

\frac{50 - 40}{40} \times 100 = 25\%

, a

25\%

increase.

Worked examples

What is

30\%

80

?
Multiply by

\frac{30}{100}

\frac{30}{100} \times 80 = 24

The number

15

is what percent of

60

?
Divide and multiply by

100

\frac{15}{60} \times 100 = 25\%

A price rises from

50

dollars to

65

dollars. What is the percentage increase?
Use

\frac{\text{final} - \text{initial}}{\text{initial}} \times 100

\frac{65 - 50}{50} \times 100 = 30\%

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