Lesson 3: The Percent Proportion

Property

A percent proportion is an equation where a percent is equal to an equivalent ratio. The amount is to the base as the percent is to 100.
$\frac{\text{amount}}{\text{base}} = \frac{\text{percent}}{100}$
We can restate this as: The amount out of the base is the same as the percent out of one hundred.

Examples

• To solve "What number is 45% of 80?", set up the proportion $\frac{n}{80} = \frac{45}{100}$. Cross-multiply to get $100n = 3600$, so $n=36$.
• To solve "6.5% of what number is 1.56 dollars?", set up $\frac{1.56}{n} = \frac{6.5}{100}$. Cross-multiply to get $156 = 6.5n$, so $n=24$.
• To solve "What percent of 72 is 9?", set up $\frac{9}{72} = \frac{p}{100}$. Cross-multiply to get $900 = 72p$, so $p=12.5$. The answer is 12.5%.

Explanation

This special proportion is a powerful tool for any percent problem. It turns sentences like "What is 25% of 80?" into an equation you can easily solve by finding the missing piece. Just fill in what you know!

Property

To find the part when you know the percent and the whole, use the percent proportion:

Cross multiply and solve for the part:

Property

To find what percent a part is of a whole using the percent proportion:
Set up the proportion

Examples