Compare Fractions Made of the Same Parts
Compare fractions with the same denominator and same whole.
Supplied materials
- Paper and pencil.
- Supplied matching strips: each has eight equal parts; one has two shaded and the other has five shaded.
Learn the idea
When denominators match, pieces have the same size if the wholes match. Five eighths has more of those same-sized pieces than two eighths. Compare numerators to compare amounts without changing the piece size.
Check the whole first. Five eighths of a tiny strip is not automatically larger than two eighths of a much larger strip. Our matching strips make the comparison valid. The symbol < means the amount on its left is smaller.
- Draw two matching strips with eight equal boxes each.
- Shade two boxes on one and five on the other.
- Write 2/8 < 5/8, then compare 3/6 and 4/6 of matching strips.
See the method in action
Two eighth-pieces cover less than five eighth-pieces: 2/8 < 5/8. The difference is three pieces, or 3/8 of the matching whole.
Check your reasoning
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See the answer and explanation
3/6 < 4/6
Both amounts count sixths of the same whole. Three sixths uses fewer equal parts than four sixths, so 3/6 < 4/6.
Take it further
Compare 5/6 and 4/6 instead. The left amount now has one more sixth, so 5/6 > 4/6. Explain what changed in the numerator.
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