GCSE Maths Number FDP Fractions

Equivalent Fractions

Equivalent Fractions

Here we will learn about equivalent fractions including how to simplify fractions.

There are also equivalent fractions worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if you’re still stuck.

What are equivalent fractions?

Equivalent fractions are fractions that have the same value
We use equivalent fractions to write a fraction in its simplest terms. To do this we look at the numerator (the top number) and the denominator (the bottom number) and find a common factor to cancel.
The numerator and denominator are always whole numbers.

Equivalent fractions can be used to compare fractions when they have different denominators so that they can be written in order of size.  

Here are some examples of the concept of equivalent fractions: 

E.g.

\[\frac{1}{2}=\frac{2}{4}\]
equivalent fractions 1

E.g.

\[\frac{2}{3}=\frac{6}{9}\]
equivalent fractions 2

How to write equivalent fractions

In order to simplify fractions:

  1. Look at the numerator and the denominator and find the Highest Common Factor.
  2. Divide both the numerator and the denominator by the HCF.
  3. Write the fraction in its simplest terms.

In order to calculate equivalent fractions:

  1. Look at the denominators in both fractions and work out the multiplier.
  2. Multiply the numerator of one of the fractions by the multiplier.
  3. Complete the second fraction.

Equivalent fractions worksheet

Equivalent fractions worksheet

Equivalent fractions worksheet

Get your free equivalent fractions worksheet of 20+ questions and answers. Includes reasoning and applied questions.

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Equivalent fractions worksheet

Equivalent fractions worksheet

Equivalent fractions worksheet

Get your free equivalent fractions worksheet of 20+ questions and answers. Includes reasoning and applied questions.

DOWNLOAD FREE

Related lessons on fractions

Equivalent fractions is part of our series of lessons to support revision on fractions. You may find it helpful to start with the main fractions lesson for a summary of what to expect, or use the step by step guides below for further detail on individual topics. Other lessons in this series include:

Equivalent fractions examples

Example 1: simplify fractions

Write the following fraction in its simplest form:

\[\frac{12}{14}\]

  1. Look at the numerator and the denominator and find the Highest Common Factor.

The numerator of the fraction is 12.

The denominator of the fraction is 14.

They are both multiples of 2. The Highest Common Factor of 12 and 14 is 2.

2Divide both the numerator and the denominator by the HCF.

\[\frac{12}{14}=\frac{6\times2}{7\times2}\]

The HCF of 2 will cancel.

The new numerator is 6 and the new denominator is 7.
6 and 7 have no common factors other than 1 so the fraction is in its simplest form.

3Write the fraction in its simplest terms.

\[\frac{12}{14}=\frac{6}{7}\]

Example 2: simplify fractions

Write the following fraction in its simplest form:

\[\frac{15}{20}\]

Look at the numerator and the denominator and find the Highest Common Factor.

Show step

Divide both the numerator and the denominator by the HCF.

Show step

Write the fraction in its simplest terms.

Show step

Example 3: simplify fractions

Write the following fraction in its simplest form:

\[\frac{24}{30}\]

Look at the numerator and the denominator and find the Highest Common Factor.

Show step

Divide both the numerator and the denominator by the HCF.

Show step

Write the fraction in its simplest terms.

Show step

Example 4: calculating equivalent fractions

Find the missing value of these equivalent fractions:

\[\frac{3}{5}=\frac{?}{20}\]

Look at the denominators in both fractions and work out the multiplier.

Show step

Multiply the numerator of one of the fractions by the multiplier.

Show step

Complete the second fraction.

Show step

Example 5: calculating equivalent fractions

Find the missing value of these equivalent fractions:

\[\frac{2}{7}=\frac{?}{21}\]

Look at the denominators in both fractions and work out the multiplier.

Show step

Multiply the numerator of one of the fractions by the multiplier.

Show step

Complete the second fraction

Show step

Example 6: calculating equivalent fractions

Find the missing value of these equivalent fractions:

\[\frac{5}{8}=\frac{?}{72}\]

Look at the denominators in both fractions and work out the multiplier.

Show step

Multiply the numerator of one of the fractions by the multiplier.

Show step

Complete the second fraction.

Show step

Common misconceptions

  • Fractions in the simplest form

You can simplify a fraction by using any of the common factors of the numerator and the denominator of a fraction. However you may need to cancel more than once to make sure you have written the fraction in its simplest form.
Using the Highest Common Factor means that you will only have to cancel once

E.g.


Write the following fraction in its simplest form.

\[\frac{20}{60}\]

20 and 60 have a common factor of 10.

\[\frac{20}{60}=\frac{2\times10}{6\times10}=\frac{2}{6}\]

However the new fraction has not been written in its simplest form as the new numerator 2 and the new denominator 6 also share a common factor of 2.

\[\frac{2}{6}=\frac{1\times2}{3\times2}=\frac{1}{3}\]

The fraction in its simplest form is 13 \frac{1}{3}

  • Equivalent fractions and common factors

You cannot make equivalent fractions by using addition.

E.g.

This is incorrect cancelling.

\[\frac{5}{10}=\frac{2+3}{7+3}=\frac{2}{7}\] ✘

This is correct cancelling.

\[\frac{5}{10}=\frac{1\times5}{2\times5}=\frac{1}{2}\] βœ”

  • Fractions and equivalence

E.g.

Because 510 \frac{5}{10} and 12 \frac{1}{2} use different numbers (they have different numerators and denominators) they appear to be different fractions, however they are actually equivalent to each other.

\[\frac{5}{10}=\frac{1\times5}{2\times5}=\frac{1}{2}\]

Practice equivalent fractions questions

1. Write the following fraction in its simplest form: 520 \frac{5}{20}

14 \frac{1}{4}
GCSE Quiz True

13 \frac{1}{3}
GCSE Quiz False

25 \frac{2}{5}
GCSE Quiz False

115 \frac{1}{15}
GCSE Quiz False
520=1Γ—54Γ—5=14 \frac{5}{20}=\frac{1\times5}{4\times5}=\frac{1}{4}

2. Write the following fraction in its simplest form: 824 \frac{8}{24}

412 \frac{4}{12}

GCSE Quiz False

26 \frac{2}{6}

GCSE Quiz False

13 \frac{1}{3}

GCSE Quiz True

512 \frac{5}{12}

GCSE Quiz False

824=1Γ—83Γ—8=13 \frac{8}{24}=\frac{1\times8}{3\times8}=\frac{1}{3}

3. Write the following fraction in its simplest form: 3648 \frac{36}{48}

68 \frac{6}{8}

GCSE Quiz False

1824 \frac{18}{24}

GCSE Quiz False

712 \frac{7}{12}

GCSE Quiz False

34 \frac{3}{4}

GCSE Quiz True

3648=3Γ—124Γ—12=34 \frac{36}{48}=\frac{3\times12}{4\times12}=\frac{3}{4}

4. Find the missing value of these equivalent fractions: 34=?24 \frac{3}{4}=\frac{?}{24}

2324 \frac{23}{24}

GCSE Quiz False

1824 \frac{18}{24}

GCSE Quiz True

1924 \frac{19}{24}

GCSE Quiz False

2124 \frac{21}{24}

GCSE Quiz False

34=3Γ—64Γ—6=1824 \frac{3}{4}=\frac{3\times6}{4\times6}=\frac{18}{24}

5. Find the missing value of these equivalent fractions: 67=?28 \frac{6}{7}=\frac{?}{28}

1828 \frac{18}{28}

GCSE Quiz False

2428 \frac{24}{28}

GCSE Quiz True

1228 \frac{12}{28}

GCSE Quiz False

2428 \frac{24}{28}

GCSE Quiz False

67=6Γ—47Γ—4=2428 \frac{6}{7}=\frac{6\times4}{7\times4}=\frac{24}{28}

6. Find the missing value of these equivalent fractions: 59=?63 \frac{5}{9}=\frac{?}{63}

3563 \frac{35}{63}  

GCSE Quiz True

2563 \frac{25}{63}

GCSE Quiz False

3063 \frac{30}{63}

GCSE Quiz False

4263 \frac{42}{63}

GCSE Quiz False

59=5Γ—79Γ—7=3563 \frac{5}{9}=\frac{5\times7}{9\times7}=\frac{35}{63}

Equivalent fractions GCSE questions

1. Here is a list of four fractions.

 

1520 \frac{15}{20}     525\frac{5}{25}      315 \frac{3}{15}      210 \frac{2}{10}

 

One of these fractions is not equivalent to 15 \frac{1}{5}

 

Write down this fraction.

(1 mark)

Show answer

1520 \frac{15}{20}

(1)

2. Here is a list of four fractions.

 

1824 \frac{18}{24}      1520 \frac{15}{20}      2840 \frac{28}{40}      3648 \frac{36}{48}

 

One of these fractions is not equivalent to 34 \frac{3}{4}

 

Write down this fraction.

(1 mark)

Show answer

2840 \frac{28}{40}

(1)

3. (a) Show that 35 \frac{3}{5} is bigger than 59 \frac{5}{9} .

 

 

(b) Find a fraction which is bigger than 35 \frac{3}{5}

but smaller than 34 \frac{3}{4} .

(4 marks)

Show answer

(a)

3Γ—95Γ—9=2745 \frac{3\times9}{5\times9}=\frac{27}{45}      5Γ—59Γ—5=2545 \frac{5\times5}{9\times5}=\frac{25}{45}

 

for converting one fraction to an equivalent fraction

(1)

 

for both fractions with a common denominator

(1)

 

35=2745 \frac{3}{5}=\frac{27}{45}      59=2545 \frac{5}{9}=\frac{25}{45}

 

(b)

3Γ—45Γ—4=1220 \frac{3\times4}{5\times4}=\frac{12}{20}      3Γ—54Γ—5=1520 \frac{3\times5}{4\times5}=\frac{15}{20}

 

for converting one fraction to an equivalent fraction

(1)

 

for a correct answer between 0.6 and 0.75

(1)

 

1320 \frac{13}{20} or 1420 \frac{14}{20} or 710 \frac{7}{10}

Learning checklist

You have now learned how to:

  • Simplify fractions
  • Write an equivalent fraction for a given fraction

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