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KS3 Ratio & Proportion

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Ratio & Proportion

Sharing in a Ratio (No Calculator) — KS3 Maths

Share an amount in a ratio: add the parts, divide the total, multiply up each share, plus the classic mistake to avoid. Free KS3 lesson.

Add the parts of the ratio, divide the total by that to get one part, then multiply up each share. £20 in 2 : 3 gives £8 and £12.

Sharing in a Ratio (No Calculator) — KS3 Maths thumbnail

Sharing in a ratio is three steps, always the same three. Add the parts to find how many shares there are altogether, divide the total by that to find what one part is worth, then multiply up to get each person's share. It works for two-way splits, three-way splits and any total you're given.

What does a ratio like 2 : 3 actually mean?

If Mia and Ben share money in the ratio 2 : 3, the money is split into parts — 2 parts for Mia and 3 parts for Ben, so 5 equal parts altogether. The ratio numbers are not the amounts themselves; they just tell you how many parts each person gets.

Order matters too. If the question says "Mia and Ben in the ratio 2 : 3", Mia is named first, so the first number belongs to her.

Worked example

Share £20 in the ratio 2 : 3

Mia and Ben wash cars together. Mia worked two hours and Ben worked three, so they share their £20 earnings in the ratio 2 : 3.

Step 1 — add the parts: $2 + 3 = 5$ parts altogether.

Step 2 — divide the total: $£20 \div 5 = £4$ , so each part is worth £4.

Step 3 — multiply up each share:

Mia has 2 parts: $2 \times £4 = £8$
Ben has 3 parts: $3 \times £4 = £12$

Check: $£8 + £12 = £20$ ✓ — exactly what they started with.

A bar of £20 cut into 5 equal parts, two shaded sage and three gold, with the three steps giving 8 : 12 — Five equal parts of £4 — and the shares add back to £20.

Worked example

Share 35 sweets in the ratio 4 : 3

Asha and Tom share a jar of 35 sweets in the ratio 4 : 3. It's the same three steps — ratios aren't just for money.

Step 1 — add the parts: $4 + 3 = 7$ parts.

Step 2 — divide the total: $35 \div 7 = 5$ sweets per part.

Step 3 — multiply up:

Asha: $4 \times 5 = 20$ sweets
Tom: $3 \times 5 = 15$ sweets

Check: $20 + 15 = 35$ ✓ — all the sweets are shared.

A jar of 35 sweets, 20 of one colour and 15 of another, with the three steps giving 20 : 15 — The jar carries the real count, so the shares are of something countable.

The golden rule doesn't change when a third person joins — you just add all the parts in step 1. It works for any number of people.

Worked example

Three-way share: £45 in the ratio 2 : 3 : 4

Jo, Raj and Zara share £45 in the ratio 2 : 3 : 4.

Step 1 — add all the parts: $2 + 3 + 4 = 9$ parts.

Step 2 — divide the total: $£45 \div 9 = £5$ per part.

Step 3 — multiply up each share:

Jo: $2 \times £5 = £10$
Raj: $3 \times £5 = £15$
Zara: $4 \times £5 = £20$

Check: $£10 + £15 + £20 = £45$ ✓

A bar of £45 cut into 9 parts and three money jars holding £10, £15 and £20, with the three steps giving 10 : 15 : 20 — A third share changes nothing — the parts just add to 9 instead of 5.

Where you'll use this next

Simplifying ratios often comes first, to make the parts easier to add.
Recipes and scaling share ingredients in a fixed ratio.
Fractions of an amount is the same divide-then-multiply move — each share is a fraction of the total.

Practice questions

Try these yourself, then click to check each answer. Every solution uses the same three steps: add the parts, divide the total, multiply up.

1.Share £18 between Amy and Sam in the ratio 1 : 2.Show answer

Add the parts: $1 + 2 = 3$ . Divide the total: $£18 \div 3 = £6$ per part.

Amy gets $1 \times £6 = £6$ and Sam gets $2 \times £6 = £12$ .

Check: $£6 + £12 = £18$ ✓

2.Share £35 in the ratio 2 : 5.Show answer

Add the parts: $2 + 5 = 7$ . Divide the total: $£35 \div 7 = £5$ per part.

The shares are $2 \times £5 = £10$ and $5 \times £5 = £25$ .

Check: $£10 + £25 = £35$ ✓

3.Share 48 sweets between Leo and Nina in the ratio 3 : 5.Show answer

Add the parts: $3 + 5 = 8$ . Divide the total: $48 \div 8 = 6$ sweets per part.

Leo gets $3 \times 6 = 18$ sweets and Nina gets $5 \times 6 = 30$ sweets.

Check: $18 + 30 = 48$ ✓

4.Share £27 in the ratio 4 : 5.Show answer

Add the parts: $4 + 5 = 9$ . Divide the total: $£27 \div 9 = £3$ per part.

The shares are $4 \times £3 = £12$ and $5 \times £3 = £15$ .

Check: $£12 + £15 = £27$ ✓

5.Share £48 between three friends in the ratio 1 : 2 : 3.Show answer

Add all the parts: $1 + 2 + 3 = 6$ . Divide the total: $£48 \div 6 = £8$ per part.

The shares are $1 \times £8 = £8$ , $2 \times £8 = £16$ and $3 \times £8 = £24$ .

Check: $£8 + £16 + £24 = £48$ ✓

6.Share £70 in the ratio 2 : 3 : 2.Show answer

Add all the parts: $2 + 3 + 2 = 7$ . Divide the total: $£70 \div 7 = £10$ per part.

The shares are $2 \times £10 = £20$ , $3 \times £10 = £30$ and $2 \times £10 = £20$ .

Check: $£20 + £30 + £20 = £70$ ✓ — two people can get the same share; that's fine.

7.Spot the mistake: a student shares £30 in the ratio 2 : 3 and gets £15 and £10. What went wrong, and what are the correct shares?Show answer

The student divided £30 by each ratio number ( $£30 \div 2 = £15$ and $£30 \div 3 = £10$ ) — the classic mistake. A quick check exposes it: $£15 + £10 = £25$ , not £30.

Correctly: add the parts ( $2 + 3 = 5$ ), divide the total ( $£30 \div 5 = £6$ per part), multiply up: $2 \times £6 = £12$ and $3 \times £6 = £18$ .

Check: $£12 + £18 = £30$ ✓

Practise this skill

A free printable worksheet with 16 questions and a full worked answer key. No sign-up needed.

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