Lesson 1: Analyze Percents of Numbers

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 ($a$) of a whole ($b$) given a percent ($p$), you can set up and solve the percent proportion:

Examples

Property

Percents are a special type of fraction with a denominator of 100. For example, if 20% of the 7th grade plans to purchase Val-o-grams on Valentine’s Day next year, this tells us that 20 out of every 100 7th graders plan to purchase a Val-o-gram. The symbol “%” is used to represent percent. So 420% means $\frac{420}{100}$, 4.20, or 420 per hundred.

Examples

• A survey shows 75% of students love pizza. This means for every 100 students, 75 love pizza, which is the same as the fraction $\frac{75}{100}$ or $\frac{3}{4}$.

• A battery is at 15% charge. This means it has $\frac{15}{100}$ of its total capacity remaining, which simplifies to $\frac{3}{20}$.