Converting Percents to Fractions

Converting Percents to Fractions | CodeSignal Learn

Introduction

Welcome back to Percent Foundations for Everyday Life! We are already on the third lesson of the course, so our percent skills are building nicely. In the first lesson we explored what percentages mean in daily life, and in the second we learned to convert between percents and decimals using a two-place shift. Today we take the next logical step: converting percents to fractions. By the end of this lesson, we will be able to rewrite any percent as a fraction in its simplest form — whole-number percents, decimal percents, and even percents greater than 100% — giving us yet another way to express and compare quantities.

Why Fractions Are a Natural Next Step

25\%

From Percent to Fraction in Two Steps

100

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As we may recall from earlier lessons, a percent is simply a number "out of 100." That phrase already sounds like a fraction: $25\%$ means $25$ out of $100$ , which is $\frac{25}{100}$ . Last time we divided that fraction to get a decimal ( $0.25$ ). This time, instead of dividing, we will simplify the fraction itself.

Fractions like $\frac{1}{4}$ are often easier to picture and work with than $25\%$ or $0.25$ , especially when we want to see at a glance that something is "a quarter" of a whole. If a news headline says "75% of voters support the measure," thinking of that as $\frac{3}{4}$ can make the size of that majority feel more concrete. Learning to move between percents and fractions gives us the flexibility to choose whichever form makes the math — or the message — clearest.

Every percent-to-fraction conversion follows the same two-step process: write the percent over 100, then simplify. The first step is straightforward — place the percent value over $100$ :

\text{Percent}\% = \frac{\text{Percent}}{100}

Here are a few quick examples of that first step:

Percent	Fraction over 100
$40\%$	$\frac{40}{100}$
$75\%$	$\frac{75}{100}$
$6\%$	$\frac{6}{100}$

The second step is where the real work happens: reducing the fraction to its simplest form. To simplify, we find the greatest common factor (GCF) of the numerator and denominator and divide both by it.

Flow diagram showing 40% changing to 40 over 100 and then to 2 over 5

Let's walk through $\frac{40}{100}$ :

The factors of $40$ include $1, 2, 4, 5, 8, 10, 20, 40$ .
The factors of $100$ include $1, 2, 4, 5, 10, 20, 25, 50, 100$ .
The greatest factor they share is $20$ .
Divide both by $20$ :

\frac{40}{100} = \frac{40 \div 20}{100 \div 20} = \frac{2}{5}

So $40\% = \frac{2}{5}$ . If spotting the GCF in one shot feels tricky, we can simplify in stages. For instance, divide $\frac{40}{100}$ by $2$ to get $\frac{20}{50}$ , then by $2$ again to get $\frac{10}{25}$ , and finally by $5$ to reach $\frac{2}{5}$ . The result is the same either way.

Benchmark Percent-Fraction Pairs

10\%

Percent	Fraction over 100	GCF	Simplest form
$10\%$	$\frac{10}{100}$	$10$	$\frac{1}{10}$
$20\%$	$\frac{20}{100}$	$20$	$\frac{1}{5}$
$25\%$	$\frac{25}{100}$	$25$	$\frac{1}{4}$
$50\%$	$\frac{50}{100}$	$50$	$\frac{1}{2}$
$75\%$	$\frac{75}{100}$	$25$	$\frac{3}{4}$
$80\%$	$\frac{80}{100}$	$20$	$\frac{4}{5}$

Introduction

Why Fractions Are a Natural Next Step

From Percent to Fraction in Two Steps

Join the 1M+ learners on CodeSignal

Benchmark Percent-Fraction Pairs

Simplifying Less Familiar Percents

Percents with a Decimal

Percents Greater than 100%

Seeing Fractions in Everyday Data

Conclusion and Next Steps