Learn the 4-Step Method
1Add the parts.
3 + 2 = 5 parts altogether.
2Find one part.
£20 ÷ 5 = £4 — the value of a single part.
3Multiply out each share.
Mia 3 × 4 = £12; Sam 2 × 4 = £8.
4Check the total.
12 + 8 = 20 ✓ — shares must rebuild the whole.
Worked Example
Share 35 sweets between two friends in the ratio 4 : 3.
3 × 5 = 15
Watch Out! Common Mistakes
Wrong divisor! Divide by the TOTAL parts (3 + 2 = 5): £4 a part → £12 and £8.
Not halves! A 3 : 2 split is deliberately unequal — 3 parts against 2.
Read the question! Some ask for one person, some for both, some for the DIFFERENCE (£12 − £8 = £4). Answer what’s asked.
⬇ Cheat Sheet
- Add the ratio numbers → total parts.
- Divide the amount by total parts → one part.
- Multiply one part by each ratio number.
- Check the shares total the original amount.
📖 Continue Your Journey
Quick summary
- Add the ratio numbers to find the total parts: 3 + 2 = 5.
- Divide the amount by total parts for one part: £20 ÷ 5 = £4.
- Multiply out: 3 parts = £12, 2 parts = £8.
- Check the shares rebuild the total: 12 + 8 = 20 ✓.
Frequently asked questions
How do you share an amount in a given ratio?
Add the ratio's parts, divide the amount by that total to value one part, then multiply by each ratio number: £20 in 3 : 2 gives £12 and £8.
What's the most common sharing-in-a-ratio mistake?
Dividing by one of the ratio numbers instead of the total parts — £20 ÷ 3 instead of £20 ÷ 5. Adding the parts first prevents it.
What if the question asks for the difference?
Work out both shares first, then subtract: £12 − £8 = £4. One extra step, same routine.
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