NumberKS3 / GCSE

Adding fractions - with different denominators

Add fractions by finding a common denominator.

  • Find a common denominator, usually the lowest common multiple of the denominators.
  • Rewrite both fractions as equivalent fractions with that denominator.
  • Add the numerators, keep the common denominator, then simplify if needed.

Example 1

Find equal-sized parts

Calculate.

Multiply the top and bottom of each changed fraction by the same number.Add the numerators; keep the denominator.

Example 2

Simplify at the end

Work out the result and simplify fully.

Multiply the top and bottom of each changed fraction by the same number.Add the numerators; keep the denominator.Highest common factor: 4.Cancel the common factor from top and bottom.

Remember
The denominator describes the size of the parts. Do not add or subtract the denominators.

Your turn

Question 1

Calculate.

Check answer
Multiply the top and bottom of each changed fraction by the same number.Add the numerators; keep the denominator.
Question 2

Calculate. Give your answer in its simplest form.

Check answer
Multiply the top and bottom of each changed fraction by the same number.Add the numerators; keep the denominator.Highest common factor: 5.Cancel the common factor from top and bottom.
Question 3

Calculate.

Check answer
Multiply the top and bottom of each changed fraction by the same number.Add the numerators; keep the denominator.
Question 4

Calculate.

Check answer
Multiply the top and bottom of each changed fraction by the same number.Add the numerators; keep the denominator.
Question 5

Calculate.

Check answer
Multiply the top and bottom of each changed fraction by the same number.Add the numerators; keep the denominator.
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