Lesson 33: Writing Percents as Fractions, Part 1

New Concept

A percent is a fraction with a denominator of 100. The word percent and its symbol, %, mean "per hundred."

What’s next

This is just the beginning. Next, you’ll walk through worked examples on how to convert any percent into a reduced fraction.

Property

A percent is actually a fraction with a denominator of 100. The word percent and its symbol, %, mean "per hundred."

Examples

$50\% = \frac{50}{100} = \frac{1}{2}$
$25\% = \frac{25}{100} = \frac{1}{4}$
$10\% = \frac{10}{100} = \frac{1}{10}$

Explanation

Think of 'percent' as a secret code for 'out of 100.' So, 50% is just a fun way of saying you have 50 out of 100 parts of a whole, like slices of a giant pizza! This makes it a fraction hiding in plain sight. Converting percents helps us easily see and compare parts of any whole.

Property

To write a percent as a fraction, we remove the percent sign and write the number as the numerator and 100 as the denominator. Then we reduce if possible.

Examples

$60\% = \frac{60}{100}$, which reduces to $\frac{60 \div 20}{100 \div 20} = \frac{3}{5}$.
$4\% = \frac{4}{100}$, which reduces to $\frac{4 \div 4}{100 \div 4} = \frac{1}{25}$.
$80\% = \frac{80}{100}$, which reduces to $\frac{80 \div 20}{100 \div 20} = \frac{4}{5}$.

Explanation

Turning a percent into a fraction is a two-step dance! First, drop the % symbol and place the number over 100 to create your fraction. But don't stop there! The grand finale is to simplify this fraction to its coolest, most reduced form. This makes the fraction much easier to work with in other math problems.

Property

The greatest common factor is the greatest number that is a factor of each of two or more numbers.

Examples

To reduce $\frac{60}{100}$, the GCF of 60 and 100 is 20, so the fraction becomes $\frac{3}{5}$.
To reduce $\frac{24}{100}$, the GCF of 24 and 100 is 4, so the fraction becomes $\frac{6}{25}$.
To reduce $\frac{75}{100}$, the GCF of 75 and 100 is 25, so the fraction becomes $\frac{3}{4}$.

Explanation

Think of the GCF as your fraction-simplifying superpower! It's the biggest number that can divide evenly into both the top and bottom numbers of a fraction. Using the GCF lets you reduce a fraction in one giant leap instead of taking lots of little baby steps. It’s the most efficient way to get your fraction to its simplest form!