## How to calculate percentages

A percentage is a fraction whose denominator (bottom number) is always 100. It is denoted using the percent sign (%) or the abbreviations pct. So 1% is 1/100. If we say 20%, we mean 20/100 = 1/5. So 25% means 1/4 and 50% means 1/2

If you have to turn a percentage into a decimal, just divide by 100. For example, 25% = 25/100 = 0.25

If you have to turn a percentage into a fraction, just add 100 as a denominator. For example, 50% = 50/100 = 1/2

The following examples show how to calculate percentages:

3 is what percent of 12?

$$3/12=1/4={1×25}/{4×25}=25/100=25%$$

What is 20% of 80?

$$80×{20/100}=80×{1/5}=16$$

8 is 40% percent of what number?

$${8×100}/40=800/40=80/4=20$$

The price of a book was increased from 10 to 12 USD. Express this increase as a percentage change of the original price.

$$Change = {Difference}/{Old;Value} ×100$$

$$={12−10}/10 ×100=2/10 ×100 = 20%$$

The price of a book was decreased from 15 to 10 USD. By what percentage did it decrease?

$$={15−10}/15 × 100=5/15 ×100 = 33.3%$$