You can only add fractions when the pieces are the same size — that is, when the denominators match. For 1/2 + 1/3, rename both as sixths: 1/2 = 3/6 and 1/3 = 2/6. Now the pieces match, so add the numerators: 3/6 + 2/6 = 5/6. You never add the denominators. Multiplying the two denominators gives a common denominator, but remember to scale each numerator by the same factor you used on its denominator. Finish by writing the answer in simplest form.
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Equal parts, equal wholes
2/4 = 4/8
Both bars are the same length. Find a division of the second bar that lines up exactly with the coloured edge.
Words to know
- common denominator
- a shared bottom number for both fractions
- numerator
- the top number you add once the bottoms match
- simplest form
- a fraction with no common factor left to cancel
Worked examples
1/2 + 1/3
- 1.Sixths: 1/2 = 3/6, 1/3 = 2/6.
- 2.Add the tops: 3/6 + 2/6 = 5/6.
= 5/6
1/4 + 1/3
- 1.Twelfths: 1/4 = 3/12, 1/3 = 4/12.
- 2.Add the tops: 3/12 + 4/12 = 7/12.
= 7/12
1/2 + 1/4
- 1.Quarters: 1/2 = 2/4.
- 2.Add the tops: 2/4 + 1/4 = 3/4.
= 3/4
For parents
Method: Rename both fractions to a common denominator, then add the tops only.
What to say: Ask 'are the pieces the same size yet?' Add only once both bottoms match.
Common mistakes:
- Adding straight across, tops and bottoms (1/2 + 1/3 → 2/5).
- Getting the common denominator but forgetting to scale the numerators (→ 2/6).