Comparing fractions, step by step
When two fractions have different bottom numbers, the larger denominator does not mean the larger fraction.
The question
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- Eighths and sevenths are different SIZES of piece, so the two top numbers cannot be compared as they stand. A bigger number on the bottom means a smaller piece — which is the part of this that feels backwards.
- Cut both into 56ths: 4/8 is 28/56, and 4/7 is 32/56. Neither has changed in size — they are just being measured in the same piece now.
- Same size of piece, so now it is only counting: 28 against 32. 4/8 is less than 4/7: 4/8 < 4/7.
How it works.
- 01
Eighths and sevenths are different SIZES of piece, so the two top numbers cannot be compared as they stand. A bigger number on the bottom means a smaller piece — which is the part of this that feels backwards.
- 02
Cut both into 56ths: 4/8 is 28/56, and 4/7 is 32/56. Neither has changed in size — they are just being measured in the same piece now.
- 03
Same size of piece, so now it is only counting: 28 against 32. 4/8 is less than 4/7: 4/8 < 4/7.