Year 6 · Mathematics
Adding and subtracting fractions with different denominators (Year 6)
You can only add or subtract fractions directly when the parts are the same size — that is, when the denominators match. When they don't, rewrite the fractions with a common denominator first.
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Try asking: “How do I add 1/2 + 1/3?”
Find a common denominator
Look for a number that both denominators divide into. The lowest one is called the lowest common denominator. For halves and thirds, it's 6, because 2 and 3 both go into 6.
Make equivalent fractions, then add
Rewrite each fraction using the common denominator, then add or subtract the numerators and keep the denominator. Simplify the answer if you can.
Worked examples
What is 1/2 + 1/3?
- Common denominator: 6.
- 1/2 = 3/6 and 1/3 = 2/6.
- 3/6 + 2/6 = 5/6.
Answer: 5/6
What is 3/4 + 1/6?
- Common denominator: 12.
- 3/4 = 9/12 and 1/6 = 2/12.
- 9/12 + 2/12 = 11/12.
Answer: 11/12
What is 2/3 − 1/4?
- Common denominator: 12.
- 2/3 = 8/12 and 1/4 = 3/12.
- 8/12 − 3/12 = 5/12.
Answer: 5/12
Common mistakes to watch for
- Adding the denominators: 1/2 + 1/3 is not 2/5 — that would be less than 1/2 on its own!
- Changing the denominator without changing the numerator to match.
Practice questions
Try these, then reveal the answers. For more questions with hints, use the tutor.
1. What is 1/4 + 1/2?
Show answer
3/4
2. What is 2/5 + 1/10?
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1/2
3. What is 5/6 − 1/3?
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1/2
4. What is 3/8 + 1/4?
Show answer
5/8
5. What is 1/3 + 1/4?
Show answer
7/12