Dividing quantities by ratio in real contexts
OCR Foundation Paper 2 and Paper 3 set ratio-sharing word problems each year. The skill is straightforward but the contexts vary widely (recipes, money, mixtures, time).
The three-step recipe
To share quantity Q in ratio a : b : c (or more parts):
- Find total parts = a + b + c.
- Find one part = Q / total parts.
- Multiply each ratio number by one-part value to get each share.
Always check that the shares add to Q.
✦Worked example— Worked example — money
Share £450 in ratio 2 : 3 : 4.
- Total parts = 9. One part = 450/9 = £50.
- Shares: 2×50, 3×50, 4×50 = £100, £150, £200.
- Check: 100 + 150 + 200 = £450 ✓.
✦Worked example— Worked example — recipe
A pancake mix uses flour : milk : eggs in ratio 4 : 3 : 1 (by volume).
To make 480 ml of mix, how much of each?
- Total parts = 8. One part = 480/8 = 60 ml.
- Flour: 4 × 60 = 240 ml. Milk: 3 × 60 = 180 ml. Eggs: 60 ml.
- Check: 240 + 180 + 60 = 480 ✓.
Reverse problem — given one share, find others or total
Example: A and B share money in ratio 5 : 7. B receives £140. Find A's share and the total.
- B's parts = 7, value £140 → one part = £20.
- A: 5 × 20 = £100. Total: A + B = £100 + £140 = £240.
Or: total = 12 parts × 20 = £240.
Combining with percentages
OCR loves multi-step ratio + percentage questions.
Example: A bag is shared between Anna, Ben, Carl in ratio 5 : 4 : 3. Anna receives £75. What is the total in the bag?
- Anna's parts = 5; one part = 75/5 = £15. Total parts = 12; total = 12 × 15 = £180.
Then: Ben's share = 4 × 15 = £60. Carl: 3 × 15 = £45.
OCR mark scheme conventions
- M1 for finding "one part".
- A1 for each correct share (or one A1 for the set).
- "Show your working" essential for full marks even if answer correct.
⚠Common mistakes
- Multiplying by total parts instead of one-part (e.g. taking 9 × 50 = 450 instead of 2 × 50 etc.).
- Forgetting to check shares sum to Q.
- Dividing the total by a single ratio part instead of the sum of parts.
- In reverse problems, dividing a given share by total parts (instead of by that share's parts).
AI-generated · claude-opus-4-7 · v3-ocr-maths-leaves