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: 

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

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

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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 $$\dfrac{1}{2}$$.​

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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:

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