Dividing quantities into ratio parts
Once you can write and simplify a ratio, the next skill is sharing a quantity in a given ratio. This appears constantly in word problems: sharing money, mixing ingredients, splitting time, etc.
The "parts" method
- Add the parts to find the total number of shares.
- Divide the quantity by the total parts → value of one part.
- Multiply each ratio number by the value of one part.
Worked example: share £60 in the ratio 2 : 3.
- Total parts: 2 + 3 = 5.
- Value of 1 part: £60 ÷ 5 = £12.
- Shares: 2 × £12 = £24, 3 × £12 = £36.
- Check: £24 + £36 = £60. ✓
- Answer: £24 and £36.
Three-part ratios
Same method extends.
Worked example: share 240 sweets in the ratio 1 : 3 : 4.
- Total: 1 + 3 + 4 = 8 parts.
- 1 part: 240 ÷ 8 = 30.
- Shares: 30, 90, 120.
- Answer: 30, 90 and 120 sweets.
When you're given one share, find the rest
Worked example: a sum of money is shared between A and B in ratio 4 : 7. A receives £36. How much does B receive, and what was the total?
- 4 parts = £36, so 1 part = £9.
- B receives 7 × £9 = £63.
- Total = (4+7) × £9 = £99.
When you're given the difference
Worked example: A and B share money in ratio 3 : 8. B has £45 more than A. How much does each have?
- Difference = 8 − 3 = 5 parts = £45 → 1 part = £9.
- A: 3 × 9 = £27; B: 8 × 9 = £72.
Real-world contexts
- Recipes — scaling ingredients up/down.
- Money sharing — inheritance, bills, profit splits.
- Mixing solutions — paint, chemicals, drinks.
- Time — splitting work hours.
⚠Common mistakes
- Using the quantity directly without finding "1 part" first.
- Adding ratio parts wrongly (e.g. saying 2 : 3 has 6 parts).
- Misreading a "difference" question as a "total".
- Forgetting to check that shares add up to the original quantity.
- Rounding too early — keep one part exact when it's a fraction.
➜Try this— Quick check
Share 84 kg in the ratio 1 : 2 : 4. Total = 7. 1 part = 12. Answer: 12, 24, 48 kg.
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