Maths · Intermediate

Adding and subtracting fractions with different denominators

To add or subtract fractions, the pieces must be the same size — the fractions need a common denominator. Then you add or subtract the numerators and keep the denominator.

Ages
9+ (rough guide)
Level
Intermediate
Subject
Maths
Time
20–30 minutes
Format
Online + printable
Stage
UK Years 5–6 · roughly US Grades 4–5
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  1. 1Learn it
  2. 2See it worked
  3. 3Try it online
  4. 4Print it
  5. 5Check your answer

Before you start

Who it's for and what to know first

Equivalent fractions and comparing fractions with a common denominator.

Learn it

How it works

  • Same denominator: add or subtract the numerators only. 2/7 + 3/7 = 5/7. The denominator does not change.
  • Different denominators: find the lowest common multiple of the denominators and convert both fractions.
  • Then add or subtract the numerators, keeping the new denominator.
  • Simplify the answer if you can.
  • If the answer is top-heavy (improper), such as 11/10, you can write it as a mixed number: 1 1/10.

Worked example 1

2/3 + 1/4

  1. The lowest common multiple of 3 and 4 is 12.
  2. 2/3 = 8/12 and 1/4 = 3/12.
  3. 8/12 + 3/12 = 11/12. This cannot be simplified.

Answer: 11/12

Worked example 2

5/6 − 1/2

  1. Use sixths: 1/2 = 3/6.
  2. 5/6 − 3/6 = 2/6.
  3. Simplify by dividing by 2.

Answer: 1/3

Try it online · print it · check it

Practice questions

Give each answer in its simplest form, for example 5/12 or 1 1/10. Type your answer, then press Check answers.

Tips

Common mistakes

  • Adding the denominators: 1/2 + 1/4 is not 2/6.
  • Forgetting to convert the numerator when you change the denominator.
  • Leaving answers unsimplified, such as 2/6 instead of 1/3.

Where next?

EasierComparing and ordering fractionsComparing fractions means deciding which of two fractions is larger.Harder / next skillPercentages of amounts‘Per cent’ means ‘out of 100’.RelatedFractions of amountsFinding a fraction of an amount means working out, for example, 3/4 of 20 sweets or 2/5 of £45.RelatedEquivalent fractionsEquivalent fractions are different-looking fractions that show the same amount.MoreAll Maths resourcesMaths resources that teach the method before the practice.

Last reviewed: 25 September 2026