To share a quantity in a ratio, add the ratio numbers to get the total number of equal parts, find the value of one part, then multiply. That three-step order is the whole skill.
What goes wrong before the steps start
The usual failure is treating the ratio numbers as if they were the amounts. A student sees 2 : 3 and divides the total by 2, then by 3. The answers do not add up to the total, but under exam pressure nobody checks.
The other failure is losing track of which part belongs to whom. Order in a ratio matters: in 2 : 3, the first name gets the 2.
The one-part method
Take a worked example. Aisyah and Hui Min share 360 stickers from a school bazaar stall in the ratio 2 : 3.
- Total parts: 2 + 3 = 5.
- One part: 360 ÷ 5 = 72.
- Aisyah: 2 × 72 = 144. Hui Min: 3 × 72 = 216.
Check by adding: 144 + 216 = 360. It matches, so the split is right.
Drawing a bar helps. Cut one long rectangle into 5 equal boxes, label 2 boxes Aisyah and 3 boxes Hui Min, and every step becomes visible.
The mistake, side by side
| Wrong approach | Correct approach |
|---|---|
| 360 ÷ 2 = 180, 360 ÷ 3 = 120 | 360 ÷ 5 = 72 per part |
| 180 + 120 = 300, not 360 | 144 + 216 = 360 |
The wrong method fails the addition check immediately. Build that check into every answer, because it takes five seconds and catches the error.
When the difference is given
Suppose Farid and Kumar share marbles in the ratio 5 : 2, and Farid has 27 more than Kumar.
The difference is 5 − 2 = 3 parts, and 3 parts = 27, so one part = 9. Farid has 45 and Kumar has 18. Check: 45 − 18 = 27, correct.
Try it yourself
A 450 g alloy contains copper and zinc in the ratio 7 : 3. Find the mass of each.
Answer
Total parts = 7 + 3 = 10. One part = 450 ÷ 10 = 45 g.
Copper = 7 × 45 = 315 g and zinc = 3 × 45 = 135 g. Check: 315 + 135 = 450 g. Keep the unit, grams, in both answers.
Where this shows up next
Ratio sharing returns in scaling a recipe-like numerical model and in mixture and concentration questions in Science. The ratio, proportion and rates hub shows the full order of skills, and the prerequisite gap finder can point to other small gaps. If you want a teacher to watch your working, see SPM Mathematics tuition.