A classic question is "share £60 between two people in the ratio 2 : 3". It comes up whenever something is split unfairly-but-fairly: dividing winnings, splitting a bill by who ate more, sharing profit between business partners. Here's a reliable method that always works.
Why this matters: real sharing is rarely 50-50. Two friends put in different amounts, so they should get different shares back. Ratio-sharing gives everyone exactly the fair slice — no arguments — and the check at the end proves nobody's been short-changed.
The method — find one "share" first
Analogy: imagine the money split into equal coins called "shares". First you work out how many shares there are and what one is worth; then you hand each person their number of shares.
- Add the ratio parts to find the total number of shares.
- Divide the amount by that total to find the value of one share.
- Multiply each part of the ratio by the value of one share.
Share £60 in the ratio 2 : 3:
• Total shares = 2 + 3 = 5.
• One share = £60 ÷ 5 = £12.
• Person A: 2 × £12 = £24. Person B: 3 × £12 = £36.
• Total shares = 2 + 3 = 5.
• One share = £60 ÷ 5 = £12.
• Person A: 2 × £12 = £24. Person B: 3 × £12 = £36.
Laid out as a table, the same three steps look like this — handy for three-part ratios too:
| Person | Parts | × one share (£12) | Amount |
|---|---|---|---|
| A | 2 | 2 × 12 | £24 |
| B | 3 | 3 × 12 | £36 |
| Total | 5 | £60 |
Always check: your answers should add back up to the original total (24 + 36 = 60 ✓).
When you're given one part, not the total
Sometimes you're told the value of a single part, or the difference between the parts, instead of the whole. The rescue is the same: work out the value of one share first, then scale.
Two numbers are in ratio 4 : 7 and the larger is 35. The 7 parts = 35, so one share = 35 ÷ 7 = 5. The smaller is 4 × 5 = 20.
Two numbers are in ratio 3 : 4 and the difference is 6. The difference is 4 − 3 = 1 part, so 1 part = 6. The numbers are 3 × 6 = 18 and 4 × 6 = 24.
Common mistake: when told "the larger is 35", don't divide 35 by the total shares. 35 is only the 7-part slice, so divide by 7, not by 11. Read carefully whether you've been given the total, one part, or the difference.
In a nutshell: add the parts, find one share, then multiply. Whatever you're given — the total, one part, or the difference — get the value of a single share first.