Learn the 4-Step Method
1Find a common denominator.
Find a number both denominators can divide into. (Use the smallest possible.)
2Make the fractions equivalent.
Change each fraction to have the denominator 6.
3Add the numerators.
Add the top numbers.
4Keep the denominator.
Write the common denominator.
Worked Example
Find 12 + 13.
Watch Out! Common Mistakes
Wrong! You must not add the denominators. Make them the same first.
Wrong! When the denominator changes, the numerator must change too: 36 + 26.
…but 6 keeps the numbers smaller and easier than 12 — and you won’t need to simplify as much at the end.
⬇ Cheat Sheet
- Find a common denominator.
- Make the fractions equivalent.
- Add the numerators.
- Keep the denominator.
Remember: same bottom, add the tops!
📖 Continue Your Journey
Quick summary
- Find a common denominator — a number both denominators divide into (use the smallest).
- Convert each fraction to an equivalent fraction with that denominator.
- Add the numerators; keep the common denominator: 1/2 + 1/3 = 3/6 + 2/6 = 5/6.
- When you change a denominator, you must change the numerator too.
Frequently asked questions
How do you add fractions with different denominators?
Find a common denominator, convert both fractions to equivalents with that denominator, then add the numerators. For example 1/2 + 1/3 = 3/6 + 2/6 = 5/6.
What is a common denominator?
A number that both denominators divide into exactly. For 2 and 3, the smallest common denominator is 6. Multiplying the two denominators together always works, but the smallest one keeps the numbers easy.
Why is 1/2 + 1/3 not 2/5?
Because you can't add pieces of different sizes by adding tops and bottoms. Halves and thirds are different-sized pieces — they must be converted to sixths (same size) before adding.
When is this taught at school?
Adding and subtracting fractions with different denominators is a Year 5–6 objective in England and appears regularly in 11+ and SATs papers.
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