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Academy11+

11+ Maths · Topic explained

Adding and subtracting fractions

What is 1/2 + 1/3? And why isn't it 2/5?

The big idea

Make the pieces the same size first (a common denominator), then add or take away the tops.

Picture it

Cut both cakes into slices of the same size, then count up the slices.

Key words

common denominator
A bottom number both fractions can share.
lowest common denominator
The smallest one: the lowest common multiple of the bottoms.
mixed number
A whole number and a fraction: 2 1/2.
improper fraction
The top is bigger than the bottom: 5/4.

Worked examples

  1. 1Warm-up

    Work out 2/7 + 3/7

    • Same-sized pieces (sevenths) already
    • Add the tops: 2 + 3 = 5
    • 5/7
  2. 211+ standard

    Work out 1/2 + 1/3

    • Common denominator: 6
    • 1/2 = 3/6 and 1/3 = 2/6
    • 3/6 + 2/6 = 5/6
  3. 311+ standard

    Work out 3/4 − 1/6

    • Common denominator: 12
    • 3/4 = 9/12 and 1/6 = 2/12
    • 9/12 − 2/12 = 7/12
  4. 411+ standard

    Work out 2 1/2 + 1 3/4

    • Wholes: 2 + 1 = 3
    • Fractions: 2/4 + 3/4 = 5/4 = 1 1/4
    • 3 + 1 1/4 = 4 1/4

The common mistake

The mistake

1/2 + 1/3 = 2/5: add the tops and add the bottoms.

Instead

1/2 + 1/3 = 3/6 + 2/6 = 5/6.

Why: The bottom number is the size of the pieces. It stays the same when you add: only the number of pieces adds up.

Where it comes up in the 11+

Adding and taking away fractions, often in stories: 'she ate 1/4, he ate 1/3: how much is left?'

The video

Video coming soon

We're making a short video that explains adding and subtracting fractions step by step. Until then, everything it covers is on this page.

Free printable

Adding and subtracting fractions worksheet

Practice questions on this topic to print and try on paper, at home or on the way to school.

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Quick quiz

Have a go first, then tap to see the answer.

  1. 1. Work out 3/8 + 1/8 in its simplest form.

    • 4/16
    • 1/2
    • 3/64
    • 1/4
    Show the answer

    1/2

    3/8 + 1/8 = 4/8 = 1/2.

  2. 2. Work out 5/6 − 1/3.

    • 4/3
    • 1/2
    • 4/6
    • 2/3
    Show the answer

    1/2

    1/3 = 2/6, so 5/6 − 2/6 = 3/6 = 1/2.

  3. 3. Sam eats 1/4 of a cake and Mia eats 1/3. What fraction is left?

    • 2/7
    • 5/12
    • 7/12
    • 1/2
    Show the answer

    5/12

    1/4 + 1/3 = 3/12 + 4/12 = 7/12 eaten; 12/12 − 7/12 = 5/12 left.