This set has twelve original questions, ordered from easier to harder, covering all five lessons in ratio and proportional reasoning. Questions 1 to 4 are warm-ups, 5 to 8 add units and fractions, and 9 to 12 mix proportion ideas.
Attempt each question on paper and write your working as you would in an exam. Open the answer only afterwards, mark the step that went wrong, and use the routing list at the end. A mistake log and retest queue helps you track which error types keep returning.
Questions
1. Share RM72 in the ratio 1:5.
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Parts: 1 + 5 = 6. One part: 72 ÷ 6 = 12.
Shares: 1 × 12 = RM12 and 5 × 12 = RM60. RM12 and RM60. Check: 12 + 60 = 72.
2. Write the ratio 45 : 60 in its simplest form.
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The highest common factor of 45 and 60 is 15. 45 ÷ 15 = 3 and 60 ÷ 15 = 4.
3 : 4.
3. Write 350 m to 1.4 km as a ratio in its simplest form.
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Convert: 1.4 km = 1400 m. Ratio 350 : 1400.
Divide both by 350: 350 ÷ 350 = 1 and 1400 ÷ 350 = 4. 1 : 4.
4. Share 240 g of sugar in the ratio 2:3:7.
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Parts: 2 + 3 + 7 = 12. One part: 240 ÷ 12 = 20 g.
Shares: 2 × 20 = 40 g, 3 × 20 = 60 g, 7 × 20 = 140 g. 40 g, 60 g, 140 g. Check: 40 + 60 + 140 = 240.
5. A recipe for 5 people uses 200 g butter and 0.75 litre milk. Find the amounts for 8 people. Give the milk in litres.
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Factor: 8 ÷ 5 = 1.6.
Butter: 200 × 1.6 = 320 g. Milk: 0.75 × 1.6 = 1.2 litres.
Check: 320 ÷ 200 = 1.6 and 1.2 ÷ 0.75 = 1.6.
6. A class of 28 has boys and girls in the ratio 3:4. Find the number of girls and the fraction of the class that are girls.
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Parts: 3 + 4 = 7. One part: 28 ÷ 7 = 4. Girls: 4 × 4 = 16. Boys: 3 × 4 = 12.
Fraction of girls: 4/7, and 4/7 of 28 = 16, which matches. 16 girls, fraction 4/7.
7. Blue and yellow paint are mixed in the ratio 5:3. A painter uses 450 ml of blue paint. How much yellow is needed, and what is the total volume?
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Blue is 5 parts, so one part = 450 ÷ 5 = 90 ml.
Yellow: 3 × 90 = 270 ml. Total: 450 + 270 = 720 ml.
8. A map has a scale of 1 : 25 000. A road is 6.4 cm long on the map. Find its real length in km.
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Real length: 6.4 × 25 000 = 160 000 cm.
160 000 cm = 1600 m = 1.6 km.
9. y is directly proportional to x.
| x | 4 | 6 | 10 |
|---|---|---|---|
| y | 14 | 21 | 35 |
Find y when x = 15, and find x when y = 77.
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k = 14 ÷ 4 = 3.5, and 21 ÷ 6 = 3.5 and 35 ÷ 10 = 3.5. So y = 3.5x.
When x = 15: y = 3.5 × 15 = 52.5. When y = 77: x = 77 ÷ 3.5 = 22.
10. Aina and Bala share money in the ratio 5:3. Aina receives RM36 more than Bala. Find the total amount and each share.
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Difference: 5 − 3 = 2 parts = RM36, so one part = RM18.
Aina: 5 × 18 = RM90. Bala: 3 × 18 = RM54. Total: RM144.
Check: 90 − 54 = 36 and 90 + 54 = 144.
11. y is inversely proportional to x.
| x | 2 | 3 | 4 |
|---|---|---|---|
| y | 12 | 8 | 6 |
Find y when x = 6, and find x when y = 1.5.
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Products: 2 × 12 = 24, 3 × 8 = 24 and 4 × 6 = 24. So y = 24/x.
When x = 6: y = 24 ÷ 6 = 4. When y = 1.5: x = 24 ÷ 1.5 = 16.
12. 15 workers complete a job in 12 days. How many workers are needed to finish it in 9 days, working at the same rate?
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Total work: 15 × 12 = 180 worker-days.
Workers needed: 180 ÷ 9 = 20 workers. Check: 20 × 9 = 180.
If you got these wrong
Match your error to the lesson that teaches it.
- Questions 1, 4, 6, 7 or 10 (wrong shares, or shares that do not add up): revisit sharing a quantity in a stated ratio. Did you divide by the sum of the parts?
- Questions 3, 5 or 8 (unit errors): revisit scaling a recipe with mixed units. Did you convert before writing the ratio?
- Question 6 (wrong fraction): revisit ratio versus fraction of the total. Is your denominator the whole, not the other part?
- Question 9 (direct proportion): revisit modelling direct proportion from a table. Did you test every pair?
- Questions 11 and 12 (inverse proportion): revisit recognising inverse proportion. Did you multiply, not divide?
- Question 2 (simplifying): practise factors in number sense and exact arithmetic.
Retest the error types a few days later with new numbers, not the same question. If one type keeps returning, a teacher can help: see online one-to-one Mathematics tuition.