Mathematics: Percentages

Percentages can be thought of as fractions that are based on a whole of 100; that is, one whole is equal to 100%. The word percent means "per hundred."

Percentage problems are often presented in three main ways:

Find what percentage of some number another number is.

- Example: What percentage of 40 is 8?
Find what number is some percentage of a given number. number is 20% of 40?
Find what number another number is a given percentage of.

- Example:
What number is 8 20% of?

There are three components in each of these cases: a whole (W), a part (P), and a percentage (%).

These are related by the equation:
.

This can easily be rearranged into other forms that may suit different questions better:

and
.

Percentage problems are often also word problems. As such, a large part of solving them is figuring out which quantities are what.

For example, consider the following word problem:
In a school cafeteria, 7 students choose pizza, 9 choose hamburgers, and 4 choose tacos. What percentage of student choose tacos?
To find the whole, you must first add all of the parts:
.

The percentage can then be found by dividing the part by the whole
):
.