Lesson 41: Finding a Percent of a Number

New Concept

When asked to find a certain percent of a number, change the percent to a fraction or a decimal before performing the calculation.

Percent to Fraction
> What number is 60% of 50?
> $n = \frac{3}{5} \times 50$

Percent to Decimal
> What number is 60% of 50?
> $n = 0.60 \times 50$

What’s next

Next, you'll master this skill through worked examples involving discounts, sales tax, and other real-world scenarios.

Property

A percent is a fraction with a denominator of 100. To change it to a decimal, shift the decimal point two places left. For a fraction, place the number over 100 and reduce.

Examples

$50\% \rightarrow \frac{50}{100} = \frac{1}{2}$
$15\% \rightarrow 0.15$
$8\% \rightarrow \frac{8}{100} = \frac{2}{25}$

Explanation

Think of the '%' sign as a disguise for '/100'. Unmask it by writing it as a fraction and simplifying, or as a decimal by moving the point. This trick makes percents easy to use in calculations!

Property

To find a percent of a number, first convert the percent to a fraction or a decimal. Then, multiply the result by the number you're finding the percentage of.

Examples

What is 75% of 20? $n = 0.75 \times 20 = 15$
How many is 80% of 25 questions? $\frac{4}{5} \times 25 = 20$ questions
Find 10% of 350 dollars: $0.10 \times 350 \text{ dollars} = 35 \text{ dollars}$

Explanation

Think of 'of' as a secret signal for 'multiply!' To find 80% of 25, just turn 80% into a friendly decimal (0.80) or fraction ($\frac{4}{5}$) and multiply away. It’s a straightforward mission to find a piece of the whole pie!