Fractions
Multiply fractions and whole numbers
Connect a fraction times a whole number with finding that fraction of an amount.
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Find a fractional part or the whole
Find a fraction of a known amount or recover an unknown whole from a given fractional part.
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Identify whether the question gives the whole or gives a fractional part. Multiply the whole by the fraction to find a part; divide the known part by the fraction to recover the whole. Check that the two quantities satisfy the stated relationship.
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What this activity builds
Distinguish the known part, the fractional relationship and the whole before choosing multiplication or division.
Worked example
Find 3/8 of 32. Then solve the reverse question: 12 is 3/8 of what number?
The part is 12; the whole in the reverse question is 32.
Three-eighths of 32 is (32 ÷ 8) × 3 = 12. Reversing the relationship gives 12 ÷ (3/8) = 12 × (8/3) = 32.
Teaching notes
Make the practice count
- Label the known number as part or whole before calculating.
- Use equal groups or a bar model to show why recovering a whole reverses finding a part.
- Check an unknown-whole answer by finding its stated fraction and comparing with the given part.
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