Mathtopus
KS3 Ratio & Proportion
KS3
Free lesson
Number
Ratio & Proportion

Sharing in a Ratio (No Calculator) — KS3 Maths

A clear, step-by-step KS3 lesson on sharing an amount in a ratio: add the parts, divide the total, multiply up each share — with coins dealt into parts, a three-way share, and the classic mistake to avoid.

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

Sharing an amount in a given ratio is one of the most common KS3 maths questions — and one of the easiest to get full marks on once you know the method. This written lesson covers exactly the same skills as the video: how to share money, sweets or anything else in a ratio like 2 : 3, how to handle a three-way share, and the classic mistake that catches so many students out. No calculator needed.

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=52 + 3 = 5 parts altogether.

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

Step 3 — multiply up each share:

  • Mia has 2 parts: 2×£4=£82 \times £4 = £8
  • Ben has 3 parts: 3×£4=£123 \times £4 = £12

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

Sharing £20 in the ratio 2 : 3 — coins dealt into two part-boxes for Mia and three for Ben, showing 2 × £4 = £8 and 3 × £4 = £12, with the check £8 + £12 = £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=74 + 3 = 7 parts.

Step 2 — divide the total: 35÷7=535 \div 7 = 5 sweets per part.

Step 3 — multiply up:

  • Asha: 4×5=204 \times 5 = 20 sweets
  • Tom: 3×5=153 \times 5 = 15 sweets

Check: 20+15=3520 + 15 = 35 ✓ — all the sweets are shared.

Sharing 35 sweets in the ratio 4 : 3 — a jar of 35 sweets with the working 4 + 3 = 7 parts, 35 ÷ 7 = 5 per part, then 4 × 5 = 20 and 3 × 5 = 15

Sharing between three people

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=92 + 3 + 4 = 9 parts.

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

Step 3 — multiply up each share:

  • Jo: 2×£5=£102 \times £5 = £10
  • Raj: 3×£5=£153 \times £5 = £15
  • Zara: 4×£5=£204 \times £5 = £20

Check: £10+£15+£20=£45£10 + £15 + £20 = £45 ✓

Sharing £45 three ways in the ratio 2 : 3 : 4 — coins fly into a jar each for Jo, Raj and Zara, showing 9 parts, £5 per part and shares of £10, £15 and £20

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=31 + 2 = 3. Divide the total: £18÷3=£6£18 \div 3 = £6 per part.

Amy gets 1×£6=£61 \times £6 = £6 and Sam gets 2×£6=£122 \times £6 = £12.

Check: £6+£12=£18£6 + £12 = £18 ✓

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

Add the parts: 2+5=72 + 5 = 7. Divide the total: £35÷7=£5£35 \div 7 = £5 per part.

The shares are 2×£5=£102 \times £5 = £10 and 5×£5=£255 \times £5 = £25.

Check: £10+£25=£35£10 + £25 = £35 ✓

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

Add the parts: 3+5=83 + 5 = 8. Divide the total: 48÷8=648 \div 8 = 6 sweets per part.

Leo gets 3×6=183 \times 6 = 18 sweets and Nina gets 5×6=305 \times 6 = 30 sweets.

Check: 18+30=4818 + 30 = 48 ✓

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

Add the parts: 4+5=94 + 5 = 9. Divide the total: £27÷9=£3£27 \div 9 = £3 per part.

The shares are 4×£3=£124 \times £3 = £12 and 5×£3=£155 \times £3 = £15.

Check: £12+£15=£27£12 + £15 = £27 ✓

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

Add all the parts: 1+2+3=61 + 2 + 3 = 6. Divide the total: £48÷6=£8£48 \div 6 = £8 per part.

The shares are 1×£8=£81 \times £8 = £8, 2×£8=£162 \times £8 = £16 and 3×£8=£243 \times £8 = £24.

Check: £8+£16+£24=£48£8 + £16 + £24 = £48 ✓

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

Add all the parts: 2+3+2=72 + 3 + 2 = 7. Divide the total: £70÷7=£10£70 \div 7 = £10 per part.

The shares are 2×£10=£202 \times £10 = £20, 3×£10=£303 \times £10 = £30 and 2×£10=£202 \times £10 = £20.

Check: £20+£30+£20=£70£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÷2=£15£30 \div 2 = £15 and £30÷3=£10£30 \div 3 = £10) — the classic mistake. A quick check exposes it: £15+£10=£25£15 + £10 = £25, not £30.

Correctly: add the parts (2+3=52 + 3 = 5), divide the total (£30÷5=£6£30 \div 5 = £6 per part), multiply up: 2×£6=£122 \times £6 = £12 and 3×£6=£183 \times £6 = £18.

Check: £12+£18=£30£12 + £18 = £30 ✓

Want more practice? Download the free worksheet below — 16 questions that build from gentle starters to three-way shares and word problems, with a full worked answer key so you can mark it together.

Practise this skill

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

Download the worksheetView worksheet details

More ratio & proportion lessons