How to simplify fractions - KS3 Maths

Key points

To a fraction, it down by dividing the and by the same number. The numerator and denominator have been written with the lowest whole number possible. This is said to be in its .
Simplified fractions have no other than 1
Knowing multiplication and division is useful for recognising common factors for division. This can be a useful skill for simplifying fractions.
Fractions can be simplified in one step using the (HCF) of the numerator and denominator.
Fractions can be simplified in more than one step by dividing by common factors other than the HCF. This method may be used if the HCF is harder to find, eg if the number is bigger.

Simplifying fractions using HCF - one step

Use division to a fraction to its .

Find the (HCF) of the numerator and denominator.
Divide both the numerator and denominator by their HCF.
The fraction has now been simplified.

Knowing multiplication and division facts may make simplifying fractions easier.

Example: simplifying fractions in one step

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$Example 1. The fraction four tenths.$
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Simplify 4⁄10
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The HCF of 4 and 10 is 2. Divide both the numerator (4) and the denominator (10) by 2. 4⁄10 reduces to 2⁄5 in its lowest terms. The numerator and denominator are the lowest possible whole numbers.
$Example 2. The fraction eight twelfths.$
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Simplify 8⁄12
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The HCF of 8 and 12 is 4. Divide both the numerator (8) and the denominator (12) by 4. 8⁄12 simplifies to 2⁄3 in its lowest terms.
$Example 3. The fraction twenty-four thirty-sixths.$
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Simplify 24⁄36
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The HCF of 24 and 36 is 12. 24⁄36 also simplifies to 2⁄3 in its lowest terms.

Simplifying fractions using common factors - more than one step

It is possible to simplify a fraction in more than one step.

Find a of the and . This must be greater than 1
Divide the numerator and denominator by that common factor.
Find another common factor greater than 1 and divide again.
Repeat this process until their only common factor is 1
The fraction is now fully simplified. The order of does not matter.

Example: more than one step

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$The fraction twenty-four thirty-sixths.$
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Simplify 24⁄36
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A common factor of 24 and 36 is 2. Divide the numerator and denominator by 2. This gives an equivalent fraction of 12⁄18
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Find another common factor. A common factor of 12 and 18 is 2. Divide the numerator and denominator by 2. This gives an equivalent fraction of 6⁄9
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The highest common factor of 6 and 9 is 3. Divide the numerator and denominator by 3. This gives the fraction in its lowest terms, 2⁄3
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24⁄36 simplifies to 2⁄3
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24⁄36 can be reduced to its lowest terms in one or more steps. The reduced fraction is always 2⁄3. The order of cancelling down does not change the outcome.

Question

Simplify $ \frac{45}{75} $

Game - Simplifying fractions

Try these questions from our Divided Islands game and practise your simplifying fractions skills.

Play the full Divided Islands game.

Practise simplifying fractions

Simplifying fractions quiz

Practise simplifying fractions with this quiz. You may need a pen and paper for your workings out.

Real-world maths

An Asian male-presenting person gesturing to a screen with lots of data and visuals. A group of colleagues with laptops and paper are sat around a table watching. — Image caption,
A data scientist may use simplest form in a report or presentation.

Simplifying fractions makes them easier to visualise and work with.

A data scientist may need to simplify fractions in their work. When collating and presenting a large amount of data, they may use fractions in their lowest terms to present their findings to make them easier to understand.

For example, they might simplify a large fraction such as $ \frac{2740}{8220} $ to $ \frac{1}{3} $. This will make their findings easier to visualise in a report.