Find a Fraction of a Fraction

Supplied materials

• Paper and pencil.
• Supplied quantity: a pretend strip is 3/4 meter long; select 2/3 of that length.

Learn the idea

A fraction of a fraction takes part of an amount that is already less than a whole. Divide the three-quarter-meter length into three equal sections. Each section is one quarter meter, so two sections total two quarters.

Multiplying records the same action: 2/3 × 3/4 = 6/12 = 1/2. The product is smaller than 3/4 because only two thirds of that positive length was selected. This helps catch an answer that is too large.

1. Draw a whole meter in four equal sections and mark three as the starting length.
2. Split that marked length into its three quarter-meter sections; choose two of them.
3. Write 2/3 × 3/4, then find 3/5 of a 2/3-meter length.

Check your reasoning

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Take it further

Select 1/5 of the same 2/3-meter length. The result is 1/5 × 2/3 = 2/15 meter, one third of the previous selected length.

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