Finding a fraction of an amount
Maths · Key Stage 2 · The School
The bottom number is a division
To find 1/4 of 20, share 20 into 4 equal groups: 20 ÷ 4 = 5. The denominator tells you how many groups to make, so it is an instruction to divide. Nothing else in the fraction does anything yet.
The top number is what you keep
For 3/4 of 20, do the same division first — 20 ÷ 4 = 5 — then keep 3 of those groups: 5 × 3 = 15. Divide by the bottom, multiply by the top, in that order. Doing it the other way round still works (3 × 20 = 60, then 60 ÷ 4 = 15) but the numbers get big fast.
Say the answer out loud as a sentence
Three quarters of twenty is fifteen. That sentence is worth saying because it makes an absurd answer obvious: if someone says three quarters of twenty is eighty, hearing it as a sentence catches what the arithmetic did not.
A quick check that costs nothing
A fraction less than one whole must give an answer smaller than what you started with. 3/4 of 20 has to be less than 20, and more than half of it, because 3/4 is more than 1/2. So the answer sits between 10 and 20 before you calculate anything. Fifteen fits; eighty does not, and neither does two.
When the amount will not divide neatly
Find 2/3 of 50. Now 50 divided by 3 is not a whole number, and that is not a mistake in the question: it is 16 remainder 2, or 16 and 2/3. Multiply by 2 and you have 33 and 1/3. Money makes it concrete: 2/3 of £50 is £33.33 with a third of a penny left over, which is one reason shop prices are chosen so the fractions land cleanly. When the amount counts people rather than pounds, round with the context in mind rather than by habit — there is no such thing as two thirds of a child, so 2/3 of a class of 50 is 34 children, not 33.33.