How to Find a Fraction of an Amount — KS3 Maths

Finding a fraction of an amount is two steps in a fixed order: divide by the bottom, then multiply by the top. The bottom number tells you how many equal parts to break the amount into; the top tells you how many of those parts to take.

What does the bottom number actually do?

It says how many equal parts to cut the amount into. The top says how many of those parts you keep.

So for $\tfrac{3}{4}$ of 24: the 4 breaks 24 into four equal parts of 6, and the 3 keeps three of them. You never need to think about it as anything more complicated than that.

What is 3/4 of 24?

$\tfrac{3}{4}$ of 24 is 18.

Worked example

Find 3/4 of 24

Divide by the bottom. Four equal parts of 24:

$24 \div 4 = 6$

So one quarter is 6.

Multiply by the top. You want three of those quarters:

$6 \times 3 = 18$

$\tfrac{3}{4} \text{ of } 24 = 18$

Sense-check it: three quarters is most of the amount, and 18 is most of 24. If your answer had come out smaller than 6, something went wrong.

Worked example

Find 2/5 of 30

Divide by the bottom: $30 \div 5 = 6$, so one fifth is 6.

Multiply by the top: $6 \times 2 = 12$.

$\tfrac{2}{5} \text{ of } 30 = 12$

Worked example

Find 5/8 of 40

Divide by the bottom: $40 \div 8 = 5$.

Multiply by the top: $5 \times 5 = 25$.

$\tfrac{5}{8} \text{ of } 40 = 25$

Here the answer is more than half, which fits — $\tfrac{5}{8}$ is just over a half.

Does the order matter?

Mathematically, no — $24 \div 4 \times 3$ and $24 \times 3 \div 4$ both give 18. In practice, divide first. Dividing first keeps the numbers small and easy: $24 \div 4 = 6$, then $6 \times 3 = 18$. Multiplying first means handling $24 \times 3 = 72$ before dividing, which is harder without a calculator and easier to slip up on.

The exception is when the division isn't exact. For $\tfrac{2}{3}$ of 20, dividing first gives $20 \div 3 = 6.66\ldots$, so multiply first instead: $20 \times 2 = 40$, then $40 \div 3 = 13\tfrac{1}{3}$.

Where you'll use this next

• Percentage of an amount is the same skill in different clothing — 25% of something is $\tfrac{1}{4}$ of it.
• Sharing in a ratio uses the same divide-then-multiply move on each share.
• Discounts, recipe scaling and problem solving all reduce to finding a fraction of an amount.

Practice questions

Divide by the bottom, then multiply by the top. Then click to check.