Fraction products beyond one whole

Extend the part-of-part model

The fraction product rule also works beyond one whole. For 5/4 × 3/2, calculate 15/8 = 17/8. Think of one and a half lots of five quarters: one lot is 11/4, half a lot is 5/8, and together they make 17/8.

A product of two positive numbers above one is larger than either factor. Use that size check: a result below one would signal an error here.

Include the whole part of a mixed number

For 21/3 × 4, first write 21/3 = 7/3. Then 7/3 × 4 = 28/3 = 91/3.

You can check by distributing over the full amount: four lots of 2 make 8, and four lots of a third make 11/3. Their total is 91/3. The expression 2 + 1/3 × 4 multiplies only the fractional part and describes a different amount.

Check your understanding 1 Predict before calculating

Find 7/6 × 9/5. Should it be greater or less than 7/6? Explain.

Your product, size prediction and reason

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It is 63/30 = 21/10 = 21/10. It is greater than 7/6 because the multiplier 9/5 is greater than one.

Use the full batch size

Check your understanding 2 Scale the complete batch amount

A recipe uses 11/2 cups of oats per batch. How much is needed for three batches? Check using the whole cups and the fractional cups separately.

Your full amount and whole-part check

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3/2 × 3 = 9/2 = 41/2 cups. Check 1 × 3 + 1/2 × 3 = 3 + 11/2 = 41/2 cups. Multiplying only the half cup would omit the three whole cups.