Colorful House of Math logo
Log in

Calculating with Percentages


You don’t always start with a whole pizza or a whole hundred dollar bill. You must also be able to find 30 % of $250, or 25 % of 700 grams of sugar, as but two examples.

You have already seen that calculating with percentages is the same as using fractions. A fraction is a part of a whole. This whole could be 700 grams of sugar, for example, and we want to know how much 25 % ( 25 100 ) of that is.

Rule

Part of a Whole

When a part is n% of a whole, you have that

part = n 100 ×whole = n ×whole 100

This is the most important rule about percentages. The rule tells you that you can swap the percent sign (%) for the fraction 1 100.

Example 1

Find out how much 25% of 700 grams of minced meat is

You write “g” for “grams” in the calculation: 25% × 700g = 25 × 700g 100 = 25 × 7g 1 = 175g

When you calculate with percentages, it’s often concerning money. For that reason, here’s an example with money:

Example 2

Find 20% of $2500

20 % of $2500 = 20 ×$2500 100 = 20 ×$25 1 = $500 You can also rely on the fact that 20% = 1 5 and write

20 % of $2500 = 1 5 ×$2500 = $500.

Think About This

You can draw your own picture of this problem to help you understand. Use hundred dollar bills, or something else of your choice.

Percentages are also used to study the ratio between a part and a whole. The fraction 3 4 can be the ratio between three croissants and a whole pack of four croissants. Here, you need to remember that

1 4 = 0.25 = 25%

This means that one croissant is 25 %, and three croissants are

3 × 25% = 75%

of all the croissants in the bag.

Rule

Percentages Express Ratios

That a part = n 100 ×whole is the same as

part whole = n 100

That means that the ratio between a part and the whole is n%.

Remember that all fractions express a ratio.

Want to know more?Sign UpIt's free!
White arrow pointing to the LeftPrevious entry
What Does Percent Mean?
Next entryWhite arrow pointing to the right
Per Mille