Rename Fractions to Compare Them
Compare unlike denominators using a common part size.
Supplied materials
- Paper and pencil.
- Supplied fractions: 3/4 and 5/8 of matching strips.
Learn the idea
Different denominators name different-sized pieces. Comparing three pieces with five is not enough when one kind is larger. Rename both amounts using one shared denominator so you can compare equal-sized pieces.
For fourths and eighths, split every fourth into two eighths. Three fourths becomes six eighths, with the shaded amount unchanged. Five eighths is already in the needed size. Both fractions must still refer to the same whole.
- Draw matching strips for 3/4 and 5/8.
- Split each fourth into two parts and write 3/4 = 6/8.
- Compare 6/8 with 5/8, then use twelfths to compare 2/3 with 3/4.
See the method in action
3/4 = 6/8, and 6/8 > 5/8, so 3/4 > 5/8. The difference is one eighth of the matching whole.
Check your reasoning
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See the answer and explanation
2/3 < 3/4
2/3 = 8/12 and 3/4 = 9/12. Eight twelfths is less than nine twelfths, so 2/3 < 3/4.
Take it further
Compare 5/6 and 3/4 instead. Rename them 10/12 and 9/12. Now 5/6 > 3/4 by one twelfth of the same whole.
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