Equivalent fractions

Years 3 to 7

Different fractions can name the same amount, and multiplying or dividing top and bottom by the same number keeps the size.

Bars of the same length. One half, two quarters and four eighths are all the same size.

For learners

Half a bar of chocolate is the same as 2 quarters, and the same as 4 eighths. These are equivalent fractions: $\frac{1}{2} = \frac{2}{4} = \frac{4}{8}$ .

To make an equivalent fraction, multiply the top and the bottom by the same number. $\frac{1}{2} \times \frac{3}{3} = \frac{3}{6}$ .

To make a fraction simpler, divide the top and the bottom by the same number. $\frac{6}{8} = \frac{3}{4}$ .

A worked example

Write $\frac{3}{5}$ with a bottom number of 20.

$5 \times 4 = 20$ , so multiply the top and bottom by 4.
$\frac{3 \times 4}{5 \times 4} = \frac{12}{20}$ .

For grown-ups

The size of a fraction does not change when you scale the pieces and the number of pieces together. Drawing bars the same length and cutting them into different numbers of parts makes this visible.

Common mistakes

Adding the same number to the top and the bottom, instead of multiplying.
Thinking a bigger bottom number means a bigger fraction.
Stopping simplifying too early. Keep dividing until the top and bottom share no factor.

Why it matters

You need equivalent fractions to add and subtract fractions, to compare them, and to understand ratios and percentages.

Topics in quarter that use this

Equivalent fractions
Comparing fractions
Fractions with the same bottom number
Adding fractions
Mixed numbers and improper fractions
Adding and subtracting mixed numbers

Fraction (Wikipedia)