Count Several Equal Fraction Lengths
Multiply a fraction by a whole number using repeated parts.
Supplied materials
- Paper and pencil.
- Supplied pretend ribbon lengths: three pieces, each 2/5 of one meter. No actual ribbon is needed.
Learn the idea
Three equal lengths of two fifths means add two fifths three times. Each piece uses the same unit, one meter. Count the total number of fifth-meter parts without changing their size.
The sum may pass one whole meter. Five fifths make one meter, so six fifths is one meter and one fifth. Multiplication records repeated addition: 3 × 2/5 = 6/5. A larger numerator than denominator can therefore describe a valid length.
- Draw three strips each showing two fifth-meter sections.
- Count 2 + 2 + 2 = 6 fifth-meter sections.
- Bundle five sections as one whole meter, then model four lengths of 3/8 meter.
See the method in action
3 × 2/5 = 2/5 + 2/5 + 2/5 = 6/5 = 1 1/5 meters. Six fifths exceed the five fifths needed for one meter.
Check your reasoning
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See the answer and explanation
3/2 meters
4 × 3/8 = 12/8 = 3/2 = 1 1/2 meters. Twelve eighth-meter parts total one and a half meters.
Take it further
Use two pieces of 3/8 meter instead. 2 × 3/8 = 6/8 = 3/4 meter, below one whole meter and half the previous total.
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