Percent

Percent is short for "per centum", which is Latin for "per hundred".

So "15 percent" (written 15%) simply means "fifteen out of a hundred."

Things don't usually come in groups of exactly 100. So, we use percents to indicate proportions. When we say 82% of North Americans drink orange juice, we mean that for each 100 North Americans, 82 drink orange juice.  We can set up a proportion to show this relationship.

Three Kinds of Percent Problems

Consider the statement "x percent of y is z."

If any two of the variables are given, you can use algebra to find out the missing one. This results in three different kinds of problems. In each one, the unknown is in a different position.

  1. problems where x is the unknown (e.g. "What percent of 44 is 11?")
  2. problems where y is the unknown (e.g. "58 is 25% of what number?")
  3. problems where z is the unknown (e.g. "What is 88% of 5000?")

Example 1:

What percent of 44 is 11?

Write a proportion.

(Note: You can reduce this fraction now if you want, but we'll be dividing anyway at the end.)

Cross-multiply.

44x = 1100

Divide.

x = 25

Example 2:

58 is 25% of what number?

Write a proportion.

Cross multiply.

25x = 5800

Divide.

x = 232

Example 3:

What is 88% of 5000?

Write a proportion.

Cross multiply.

100x = 440000

Divide.

x = 4400

Converting Percents to Decimals

To convert a percent to a decimal, just remove the % sign and multiply by 100. The quick way to do this is to move the decimal point two places to the left.

Example:

Express 2.5% as a decimal.

Move the decimal point two places to the left.

2.5% = 0.025

Converting Decimals to Percents

To convert a decimal to a percent, do just the opposite; add a percent sign and divide by 100. The quick way to do this is to move the decimal point two places to the right.

Example:

Express 1.005 as a percent.

Move the decimal point two places to the right.

1.005 = 100.5%