# Subtracting Fractions

Here we will learn about subtracting fractions including how to subtract fractions with the same denominator and with unlike denominators (different denominators), and how to subtract mixed numbers.
There are also subtracting 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 is subtracting fractions?

Subtracting fractions is when we take away one fraction from another or we find the difference between fractions.

To subtract fractions they need to have the same denominator (the same bottom numbers).
Then we can subtract the fractions by subtracting the numerators (the top numbers) and keeping the denominator the same.

The method for subtracting fractions can be modified to add fractions.

E.g.

## How to subtract fractions

In order to subtract fractions:

1. Look at the denominators (bottom numbers) to see if they have a common denominator.
2. Subtract the numerators (top numbers).
3. Write your answer as a fraction, making sure it is in its simplest form.

### Related lessons on fractions

Subtracting 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:

## Subtracting fractions examples

### Example 1: subtracting fractions with a common denominator

Work out

$\frac{3}{5}-\frac{1}{5}$

1. Look at the denominators (bottom numbers) to see if they have a common denominator.

5 is the denominator for both fractions, so 5 is the common denominator.

2Subtract the numerators (top numbers).

$\frac{3}{5}-\frac{1}{5}=\frac{3-1}{5}=\frac{2}{5}$

3Write your answer as a fraction, making sure it is in its simplest form.

$\frac{2}{5}$

2 and 5 do not have a common factor so the fraction cannot be simplified. This fraction is in its simplest form.

### Example 2: subtracting fractions with a common denominator

Work out

$\frac{5}{8}-\frac{3}{8}$

Look at the denominators (bottom numbers) to see if they have a common denominator.

Subtract the numerators (top numbers).

Write your answer as a fraction, making sure it is in its simplest form.

### Example 3: subtracting fractions with different denominators

Work out

$\frac{3}{4}-\frac{2}{5}$

Look at the denominators (bottom numbers) to see if they have a common denominator.

Subtract the numerators (top numbers).

Write your answer as a fraction, making sure it is in its simplest form.

### Example 4: subtracting fractions with different denominators

Work out

$\frac{5}{6}-\frac{1}{2}$

Look at the denominators (bottom numbers) to see if they have a common denominator.

Subtract the numerators (top numbers).

Write your answer as a fraction, making sure it is in its simplest form.

### Example 5: subtracting mixed numbers

Work out

$2\frac{1}{2}-1\frac{1}{3}$

Look at the denominators (bottom numbers) to see if they have a common denominator.

Subtract the numerators (top numbers).

Write your answer as a fraction, making sure it is in its simplest form.

### Example 6: subtracting mixed numbers

Work out

$3\frac{1}{2}-1\frac{3}{5}$

Look at the denominators (bottom numbers) to see if they have a common denominator.

Subtract the numerators (top numbers).

Write your answer as a fraction, making sure it is in its simplest form.

### Common misconceptions

• Subtracting numerators
When subtracting fractions with common denominators, only the numerators are subtracted.
E.g.
$\frac{5}{7}-\frac{2}{7}=\frac{5-2}{7}=\frac{3}{7}$

• Mixing up addition and subtraction

Sometimes we can get so involved in making sure the fractions have a common denominator that we forget it is a subtraction.

E.g

$\frac{3}{5}-\frac{1}{4}=\frac{12}{20}-\frac{5}{20}=\frac{12+5}{20}=\frac{17}{20}$

This would be wrong as the question has turned into an addition question.

• Remember to use the correct order of operations

When there is addition and subtraction in the same maths sentence, perform the operations in order from left to right as you read them.

E.g.

$\frac{6}{8}-\frac{1}{8}+\frac{2}{8}=\frac{6-1+2}{8}=\frac{7}{8}$

The correct order is 6 – 1 and then + 2.

### Practice Subtracting fractions questions

1. Work out \frac{2}{5}-\frac{1}{5}

\frac{3}{5}

\frac{1}{5}

\frac{1}{0}

\frac{2}{5}
\frac{2}{5}-\frac{1}{5}=\frac{2-1}{5}=\frac{1}{5}

2. Work out \frac{3}{8}-\frac{1}{8}

\frac{2}{5}

\frac{2}{0}

\frac{2}{8}

\frac{1}{4}
\frac{3}{8}-\frac{1}{8}=\frac{3-1}{8}=\frac{2}{8}=\frac{1}{4}

3. Work out \frac{4}{5}-\frac{1}{2}

\frac{3}{10}

\frac{3}{3}

\frac{9}{10}

\frac{1}{5}
\frac{4}{5}-\frac{1}{2}=\frac{8}{10}-\frac{5}{10}=\frac{8-5}{10}=\frac{3}{10}

4. Work out \frac{5}{8}-\frac{1}{4}

\frac{1}{8}

\frac{4}{4}

\frac{3}{8}

\frac{3}{12}
\frac{5}{8}-\frac{1}{4}=\frac{5}{8}-\frac{2}{8}=\frac{5-2}{8}=\frac{3}{8}

5. Work out 2\frac{3}{4}-1\frac{1}{3}

4\frac{1}{12}

2\frac{5}{12}

1\frac{5}{12}

1\frac{7}{12}
2\frac{3}{4}-1\frac{1}{3} =\frac{11}{4}-\frac{4}{3} =\frac{33}{12}-\frac{16}{12} =\frac{33-16}{12} =\frac{17}{12} =1\frac{5}{12}

6. Work out 2\frac{1}{5}-1\frac{2}{3}

1\frac{1}{2}

3\frac{13}{15}

1\frac{8}{15}

\frac{8}{15}
2\frac{1}{5}-1\frac{2}{3} =\frac{11}{5}-\frac{5}{3} =\frac{33}{15}-\frac{25}{15} =\frac{33-25}{15} =\frac{8}{15}

### Subtracting fractions GCSE questions

1. Work out

\frac{4}{5}-\frac{1}{3}

(2 marks)

\frac{4}{5}-\frac{1}{3}=\frac{12}{15}-\frac{5}{15}

For using a correct common denominator with at least one correct fraction

(1)

=\frac{7}{12}

(1)

2. Work out

2\frac{5}{8}-1\frac{1}{3}

(2 marks)

2\frac{5}{8}-1\frac{1}{3}=\frac{21}{8}-\frac{4}{3}=\frac{63}{24}-\frac{32}{24}

For using a correct common denominator with at least one correct fraction

(1)

\frac{63}{24}-\frac{32}{24}=\frac{31}{24}=1\frac{7}{24}

(1)

3. Which of these two fractions is closer to 1?
You must show all your working.

\frac{7}{4}     \frac{4}{7}

(3 marks)

\frac{7}{4}=\frac{49}{28}
and
\frac{4}{7}=\frac{16}{28}

For writing fractions with a common denominator

(1)

\frac{49}{28}-\frac{28}{28}=\frac{21}{28}
and
\frac{28}{28}-\frac{16}{28}=\frac{12}{28}

For finding the difference of the fractions to 1

(1)

\frac{12}{28} is the smallest difference,

So \frac{4}{7} is closer to 1.

For the correct answer with workings

(1)

## Learning checklist

You have now learned how to:

• Subtract fractions with the same denominator
• Subtract fractions with different denominators
• Subtract mixed numbers

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