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Comparing fractions with different denominators
Comparing 2/5 and 1/3 is hard because the pieces are different sizes. There are three reliable methods, and it's worth knowing all three because each is fastest in different situations.
Three methods, with examples
- Common denominator. Rewrite both with the same bottom number. 2/5 = 6/15 and 1/3 = 5/15, so 2/5 > 1/3.
- Benchmark 1/2. Compare each fraction to one half. 3/8 is less than half (half of 8 is 4) and 4/7 is more than half, so 3/8 < 4/7.
- Cross-multiply. For 5/6 and 7/9: 5 × 9 = 45 and 6 × 7 = 42. The bigger product goes with 5/6, so 5/6 > 7/9.
6 comparing questions (use <, > or =)
- 2/3 ◯ 3/5
- 3/8 ◯ 1/2
- 4/5 ◯ 5/6
- 2/4 ◯ 3/6
- 7/10 ◯ 2/3
- 1/6 ◯ 2/9
Use <, > or = for the ◯.
Show answers
- 2/3 > 3/5
- 3/8 < 1/2
- 4/5 < 5/6
- 2/4 = 3/6
- 7/10 > 2/3
- 1/6 < 2/9
Tips for parents
- Start with the benchmark method. It builds number sense.
- Use the common denominator method to show why the answer is right.
- Watch for the belief that bigger numbers mean a bigger fraction. 1/8 is smaller than 1/3.