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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  1. 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.
  2. 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.
  3. 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.

  1. 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.

  2. 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.

  3. 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.