How do you add fractions with different denominators?
Short answer
Make the denominators the same first. Find a common denominator (the lowest common multiple is easiest), change each fraction to an equivalent fraction with that denominator, then add the numerators and keep the denominator. For example, 1/3 + 1/4 = 4/12 + 3/12 = 7/12.
Step by step
- Look at the two denominators and find the smallest number both divide into.
- Change each fraction: whatever you multiply the bottom by, multiply the top by the same number.
- Add the numerators. The denominator stays the same.
- Simplify the answer if you can, and change top-heavy fractions to mixed numbers if asked.
Worked example
Work out 2/5 + 3/10
- 10 is a multiple of 5, so use 10 as the denominator
- 2/5 = 4/10
- 4/10 + 3/10 = 7/10
Common mistakes
- Adding the denominators: 1/3 + 1/4 is not 2/7.
- Changing the denominator without changing the numerator.
- Forgetting to simplify, for example leaving 6/8 instead of 3/4.
Useful for:KS2 SATsCommon EntranceCPE
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