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Equivalent fractions

Tutor: Toby

# Equivalent fractions

## In a nutshell

Equivalent fractions are fractions which represent the same amount.  They may look different, but are actually worth the same.

##### Example 1

The fractions represented below are equivalent fractions.

 ​$\frac{1}{4}$​​ ​$\frac{2}{8}$​​

## Finding equivalent fractions

To find fractions that are equivalent, you can multiply or divide the top and bottom numbers by the same number.

##### Example 2

These fractions are all equivalent to one half.

### Multiplying to find equivalent fractions

Multiply the numerator and the denominator by the same number.

##### Example 3

Give a fraction that is equivalent to $\dfrac{1}{2}$

You can multiply the numerator and denominator by $2$. For example:

$\frac{1}{2}=\dfrac{1\times2}{2\times2}=\dfrac{2}{4}$

So, $\dfrac{2}{4}$ is equivalent to $\dfrac{1}{2}$.​

​​

### Dividing to find equivalent fractions

Divide the numerator and the denominator by the same number.

##### Example 4

Give a fraction that is equivalent to $\dfrac{4}{8}$

You can divide the numerator and denominator by $4$. For example:

$\dfrac{4}{8}=\dfrac{4\div4}{8\div4}=\dfrac{1}{2}$

So, $\dfrac{4}{8}$ is equivalent to $\dfrac{1}{2}$.​

​​

##### Example 5

Which of the following fractions are equivalent?

$\frac{2}{3}, \frac{5}{9}, \frac{6}{9}$​​

Multiply the numerator and denominator by the same number so all fractions have the same denominator:

$\frac{2\times3}{3\times3}=\frac{6}{9}$​​

Note which fractions now have the same numerator and denominator:

$\underline{\frac{2}{3}=\frac{6}{9}}$​​

##### Example 6

Which of the following fractions are equivalent?

$\frac{10}{25}, \frac{3}{5}, \frac{15}{25}$​​

Divide the numerator and denominator by the same number so all fractions have the same denominator.

$\dfrac{10\div5}{25\div5} = \dfrac{2}{5}$​​

$\dfrac{15\div5}{25\div5}=\dfrac{3}{5}$​​

Note which fractions now have the same numerator and denominator:

$\underline{\frac{3}{5}=\frac{15}{25}}$​​

## FAQs - Frequently Asked Questions

### What are equivalent fractions?

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