To compare fractions with different denominators, you cannot just look at the top or the bottom on its own. A bigger denominator means the pieces are smaller, so 1/5 is less than 1/3. The safe method is to rename both fractions with a common denominator, then compare the numerators. For 2/3 and 3/5, use fifteenths: 2/3 = 10/15 and 3/5 = 9/15. Now 10/15 is larger, so 2/3 is larger. Multiplying the two denominators together always gives a common denominator you can use.
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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
- unlike fractions
- fractions with different denominators
- common denominator
- a shared bottom number both fractions can be written with
- compare
- decide which is larger or smaller
Worked examples
Which is larger, 2/3 or 3/5?
- 1.Common denominator 15: 2/3 = 10/15, 3/5 = 9/15.
- 2.10 > 9, so 2/3 is larger.
= 2/3
Which is larger, 1/2 or 1/3?
- 1.Common denominator 6: 1/2 = 3/6, 1/3 = 2/6.
- 2.3 > 2, so 1/2 is larger.
= 1/2
Which is larger, 3/4 or 2/3?
- 1.Common denominator 12: 3/4 = 9/12, 2/3 = 8/12.
- 2.9 > 8, so 3/4 is larger.
= 3/4
For parents
Method: Rename both to a common denominator, then compare tops.
What to say: Cut a sandwich into 3 versus 5 — more cuts make smaller pieces, so 1/5 is smaller than 1/3.
Common mistakes:
- Thinking a bigger denominator makes a bigger fraction (1/5 > 1/3).
- Picking the bigger numerator without matching the denominators first.