Fractions of amounts
Objective. Find fractions of quantities and solve reverse problems.
- 1. Learn
- 2. Worked example
- 3. Practice
- 4. Feedback
- 5. Continue
Learn: the key idea
Finding a fraction of an amount means dividing the amount by the denominator, then multiplying by the numerator. For example, to find 3/5 of 40, divide 40 by 5 to get 8, then multiply by 3 to get 24. Reverse problems work backwards: if you know 3/5 of a number is 24, divide 24 by 3 to find one fifth, then multiply by 5 to recover the whole amount. These two operations — dividing by the denominator and multiplying by the numerator — always appear together when finding a fraction of a quantity.
Worked example
A charity raised £72, and 5/8 of it came from a raffle. How much came from the raffle, and what was the total amount if the raffle money alone had been £72?
- 1Divide £72 by the denominator 8: 72÷8=9.
- 2Multiply by the numerator 5: 9×5=45.
- 3So 5/8 of £72 is £45 from the raffle.
- 4For the reverse part, if £72 is 5/8 of a total, divide by 5 then multiply by 8: 72÷5×8=115.2.
Answer: £45 from the raffle; total would be £115.20
Concept mastery
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Practice
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Start practisingCommon mistake. Pupils sometimes multiply by the denominator instead of dividing, turning 2/3 of 18 into 18×3=54 rather than 12. Always divide by the denominator first, then multiply by the numerator.
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