Fractions with different denominators
You learn to add and subtract fractions that have different numbers below the line.
How to work it out
- Make denominators equal before adding or subtracting.
- Multiply numerator and denominator of each fraction by the other denominator.
- Add or subtract numerators.
A worked example
12 + 13
- Multiply the top and the bottom of 12 by 3: 36.
- Multiply the top and the bottom of 13 by 2: 26.
- Add the tops: 3 + 2 = 5.
- It is 56.
More examples
12 + 14
- Multiply the top and the bottom of 12 by 4: 48.
- Multiply the top and the bottom of 14 by 2: 28.
- Add the tops: 4 + 2 = 6, so 68.
- Simplify it: it is 34.
34 − 13
- Multiply the top and the bottom of 34 by 3: 912.
- Multiply the top and the bottom of 13 by 4: 412.
- Subtract the tops: 9 − 4 = 5.
- 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.