Converting Fractions to Percents

Introduction

Welcome back to Percent Foundations for Everyday Life! This is the fourth lesson in our course, which means we are halfway through. So far we have explored what percents mean in daily life, learned to shift between percents and decimals, and mastered turning percents into simplified fractions. Today we flip the direction: converting fractions to percents.

This skill comes up whenever information is given as a fraction and we need a percent to compare it with other data or communicate it more clearly. By the end of this lesson, we will know two reliable methods for making this conversion and will be able to handle fractions that produce clean results as well as ones that lead to repeating decimals.

Thinking in Reverse

In the previous lesson, converting a percent to a fraction meant writing the percent over $100$ and simplifying. Going the other way, our goal is the opposite: start with a fraction and figure out how many hundredths it represents, since a percent is always a number out of $100$ .

Consider $\frac{3}{4}$ . We want to know what that fraction equals when the denominator is . If we can answer that question, we have our percent. There are two clean paths to get there, and we will learn both so we can pick whichever one is faster for a given fraction.

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Denominator	Multiplier ( $k$ )	Denominator $\times k$
$2$	$50$	$100$
$4$

Fraction	Equivalent Fraction	Percent
$\frac{1}{2}$	$\frac{1 \times 50}{2 \times 50} = \frac{50}{100}$	$50\%$
$\frac{1}{4}$	$\frac{1 \times 25}{4 \times 25} = \frac{25}{100}$
$\frac{3}{4}$	$\frac{3 \times 25}{4 \times 25} = \frac{75}{100}$
$\frac{1}{5}$	$\frac{1 \times 20}{5 \times 20} = \frac{20}{100}$
$\frac{2}{5}$	$\frac{2 \times 20}{5 \times 20} = \frac{40}{100}$
$\frac{3}{5}$	$\frac{3 \times 20}{5 \times 20} = \frac{60}{100}$
$\frac{1}{10}$	$\frac{1 \times 10}{10 \times 10} = \frac{10}{100}$