Count Unit-Fraction Pieces in a Whole Length
Divide a whole-number length by a unit fraction.
Supplied materials
- Paper and pencil.
- Supplied pretend roll: 2 meters; each piece is 1/4 meter. No real cutting is needed.
Learn the idea
Division can ask how many equal-size pieces fit in a given amount. There are four quarter-meter pieces in one meter. In two meters, there are two groups of four pieces. The answer counts pieces rather than meters.
The calculation is 2 ÷ 1/4 = 8. Dividing by a size smaller than one can produce a count larger than the starting number of meters. Check by multiplying the piece count by the piece length to rebuild the total length.
- Draw two whole meters, each divided into four equal sections.
- Count all eight quarter-meter pieces.
- Check 8 × 1/4 = 2, then model three meters divided into half-meter pieces.
See the method in action
2 ÷ 1/4 = 8 pieces. The check is 8 × 1/4 = 8/4 = 2 meters, so all the original length is accounted for.
Check your reasoning
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See the answer and explanation
6 pieces
Each meter holds two half-meter pieces. Three meters hold six: 3 ÷ 1/2 = 6. Checking 6 × 1/2 = 3 confirms the total.
Take it further
Use 1/3-meter pieces in the same three-meter roll. Each meter holds three, so 3 ÷ 1/3 = 9 pieces; 9 × 1/3 = 3 meters.
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