Multiply Mixed-Number Measures Exactly

Supplied materials

• Paper and a pencil; drawing and spoken explanations are welcome. An adult may read directions and options aloud.
• Supplied worked-case record: A model rectangle has sides 1 1/2 m and 2 1/3 m.
• All quantities and shape descriptions are supplied in the worked example and questions; no purchase or personal information is needed.

Learn the idea

A mixed number can be renamed as an improper fraction by counting all of its denominator-sized parts. Multiply numerator counts and denominator sizes, then simplify or write a mixed result. In an area context, multiplying two side lengths produces square units rather than another side length.

Rename both supplied mixed numbers as fractions. Multiply their numerators and denominators, simplify, and interpret the result with the appropriate unit. Check its scale by bracketing each factor between nearby whole numbers.

A whole equals denominator-many fractional parts when renaming. Do not multiply whole parts and fraction parts separately while ignoring their cross-products. Draw an area model and label each side with both mixed and improper-fraction forms.

1. Draw an area model and label each side with both mixed and improper-fraction forms.
2. Follow the worked example. Point to each number or shape feature and say what it tells you.
3. Rename both supplied mixed numbers as fractions.
4. Try the question and then the three practice questions. Check your answers and explain any change you make.

Check your reasoning

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Take it further

Find area for 2 1/4 by 1 2/3. Expected: 15/4=3 3/4 square units.

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