# 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:*

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