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Chapter overview

Learning goals

Maths

Equivalent fractions

Your lesson progress

Summary

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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.

$Maths; Fractions; KS2 Year 3; Equivalent fractions$	$Maths; Fractions; KS2 Year 3; Equivalent fractions$
$\frac{1}{4}$	$\frac{2}{8}$

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.

Procedure

Multiply to find equivalent fractions	Divide to find equivalent fractions
Multiply the numerator and the denominator by the same number.	Divide the numerator and the denominator by the same number.
$\frac{1}{2}=\frac{1\times2}{2\times2}=\frac{2}{4}$	$\frac{4}{8}=\frac{4\div4}{8\div4}=\frac{1}{2}$
$\frac{2}{3}=\frac{2\times3}{3\times3}=\frac{6}{9}$	$\frac{3}{6}=\frac{3\div3}{6\div3}=\frac{1}{2}$

Example 3

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 4

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:

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

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.

$Maths; Fractions; KS2 Year 3; Equivalent fractions$	$Maths; Fractions; KS2 Year 3; Equivalent fractions$
$\frac{1}{4}$	$\frac{2}{8}$

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

Maths; Fractions; KS2 Year 3; Equivalent fractions

These fractions are all equivalent to one half.

Procedure

Multiply to find equivalent fractions	Divide to find equivalent fractions
Multiply the numerator and the denominator by the same number.	Divide the numerator and the denominator by the same number.
$\frac{1}{2}=\frac{1\times2}{2\times2}=\frac{2}{4}$	$\frac{4}{8}=\frac{4\div4}{8\div4}=\frac{1}{2}$
$\frac{2}{3}=\frac{2\times3}{3\times3}=\frac{6}{9}$	$\frac{3}{6}=\frac{3\div3}{6\div3}=\frac{1}{2}$

Example 3

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 4

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:

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

Frequently Asked Questions (FAQ)

FAQs

Question: How to find equivalent fractions step by step.

Answer: To find fractions that are equivalent, you can multiply or divide the top and bottom numbers by the same number.
Question: How do you find equivalent fractions?

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

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

Theory

Exercises

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Equivalent fractions

Equivalent fractions

In a nutshell

Example 1

Finding equivalent fractions

Example 2

Procedure

Example 3

Example 4

​15÷525÷5=35\dfrac{15\div5}{25\div5}=\dfrac{3}{5}25÷515÷5​=53​​​

Equivalent fractions

In a nutshell

Example 1

Finding equivalent fractions

Example 2

Procedure

Example 3

Example 4

​15÷525÷5=35\dfrac{15\div5}{25\div5}=\dfrac{3}{5}25÷515÷5​=53​​​

Now you’ve read the summary, have a go at the exercises!

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

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