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Fractions with different denominators

You learn to add and subtract fractions that have different numbers below the line.

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How to work it out

  1. Make denominators equal before adding or subtracting.
  2. Multiply numerator and denominator of each fraction by the other denominator.
  3. Add or subtract numerators.

A worked example

12 + 13

  1. Multiply the top and the bottom of 12 by 3: 36.
  2. Multiply the top and the bottom of 13 by 2: 26.
  3. Add the tops: 3 + 2 = 5.
  4. It is 56.
More examples

12 + 14

  1. Multiply the top and the bottom of 12 by 4: 48.
  2. Multiply the top and the bottom of 14 by 2: 28.
  3. Add the tops: 4 + 2 = 6, so 68.
  4. Simplify it: it is 34.

34 − 13

  1. Multiply the top and the bottom of 34 by 3: 912.
  2. Multiply the top and the bottom of 13 by 4: 412.
  3. Subtract the tops: 9 − 4 = 5.
  4. It is 512.

Watch out

  • You add the tops and the bottoms: 12 + 13 becomes 25.

    25 is less than 12, so that cannot be right. Make the pieces equal first.

  • You only change the number below the line: 12 becomes 16.

    Whatever you do to the bottom, do to the top too. 12 becomes 36.

Tips

  • Find a number that both denominators go into, like 12 for 3 and 4.

Why it works

A half and a third are different-sized pieces, so you cannot just add them. If you turn them both into sixths, the pieces are equal. Then you just add the pieces.