POP

G2.4 Finding a Fraction of an Amount

Image · 914 × 270

01 — Explanation

How do I find a unit fraction of an amount?

A unit fraction has numerator 1 (e.g. $\tfrac{1}{4}$ ). Finding a unit fraction of an amount is simply division by the denominator.

\tfrac{1}{8}\text{ of }72 = 72 \div 8 = 9

These are usually worth 1 mark (B1), awarded for the correct answer alone.

02 — Explanation

How do I find a non-unit fraction of an amount?

Use the two-step method: divide by the denominator, then multiply by the numerator. The division finds the value of one part; the multiplication scales it up to however many parts you need.

\tfrac{2}{5}\text{ of }40: \quad 40 \div 5 = 8, \qquad 8 \times 2 = 16

Why it works

dividing by the denominator finds $\tfrac{1}{5}$ of the amount; since you want 2 of those fifths, you double it. Thinking of it this way — rather than as a memorised rule — stops you from accidentally swapping which number you divide by.

Exam Tip

these are usually worth 2 marks: M1 for showing the complete method (e.g. $72 \div 6 \,(=12)$ and $12 \times 5$ ), A1 for the correct final answer. Writing both lines of working protects your mark even if the final multiplication contains a slip.

03 — Explanation

How do I use this in a word problem with an extra step?

Read to the end of the question before calculating — many problems ask for the amount remaining, not the fraction itself.

Example: There are 40 apples in a crate. $\tfrac{3}{10}$ are bad. How many good apples are there?

Bad apples: $40 \div 10 = 4$ , then $4 \times 3 = 12$ .
Good apples: $40 - 12 = 28$ .

A student who stops after step 1 and writes "12" has answered a different question and scores M1 A0 — always re-read the final command phrase before writing your answer.

04 — Worked example

Worked exam-style question

Harry has 50 sweets. He gives $\tfrac{2}{5}$ of them to Sandra and $\tfrac{3}{10}$ of them to Jamie. He keeps the rest for himself. How many sweets does Harry keep?

Sandra's share: $50 \div 5 = 10$ , then $10 \times 2 = 20$ .
Jamie's share: $50 \div 10 = 5$ , then $5 \times 3 = 15$ .
Total given away: $20 + 15 = 35$ .
Harry keeps: $50 - 35 = 15$ .

Answer: Harry keeps 15 sweets.

Common Mistake

Reversing the algorithm — multiplying by the denominator and dividing by the numerator (e.g. computing $40\times10\div3$ instead of $40\div10\times3$ ). If you're ever unsure, picture a bar split into the number of pieces given by the denominator: that step is always the division.

05 — Explanation

How does this connect to percentages and ratios?

A percentage is just a fraction out of 100, so "find 17% of 300" uses exactly the same two-step logic as a fraction question: divide by 100, then multiply by 17. Ratio-sharing problems (e.g. "share 60 in the ratio 2:3") also reduce to this skill once you find the total number of parts ( $2+3=5$ ) — the problem becomes finding $\tfrac{2}{5}$ and $\tfrac{3}{5}$ of 60.