Last reviewed: 25 October 2026
Ratio and proportion questions turn up in Mathematics papers in many forms: sharing money, mixing ingredients, map scales, speed and comparing prices. The ideas are simple once the method is clear. This guide explains each type with worked examples a junior school learner can follow on their own. Compound proportions and rates of work form a Numbers sub-strand in KICD’s Grade 9 Mathematics curriculum design.
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What a Ratio Is
A ratio compares two or more quantities of the same kind. If a class has 15 boys and 20 girls, the ratio of boys to girls is 15:20. Order matters: girls to boys is 20:15. Ratios have no units, but the quantities must be in the same unit before you compare them. The ratio of 50 cm to 2 m is 50:200, not 50:2.
Simplifying Ratios
Divide all parts by their highest common factor. 15:20 simplifies to 3:4. 12:18:24 simplifies to 2:3:4. With decimals or fractions, multiply first to make whole numbers: 1.5:2 becomes 3:4, and ½:⅓ becomes 3:2 after multiplying both by 6.
Sharing in a Given Ratio
Add the parts, find the value of one part, then multiply.
- Share KSh 3,600 between Achieng and Baraka in the ratio 5:4. Total parts = 9. One part = 400. Achieng gets KSh 2,000 and Baraka KSh 1,600.
- Three sisters share 84 mangoes in the ratio 2:3:7. Total parts = 12, one part = 7, so they get 14, 21 and 49.
Check that the shares add up to the original total. It is a quick and reliable test.
Finding a Quantity From a Ratio
If the ratio of boys to girls is 3:5 and there are 24 boys, then one part is 8, so there are 40 girls and 64 learners altogether. When a question gives the difference between shares, use that: if the shares are in the ratio 7:3 and differ by KSh 800, the difference of 4 parts is 800, so one part is 200.
Direct Proportion
Two quantities are in direct proportion when one doubles as the other doubles. If 4 exercise books cost KSh 240, one costs KSh 60 and 7 cost KSh 420. This “find one, then multiply” approach is called the unitary method and works for almost any direct proportion question.
Inverse Proportion
Here, as one quantity goes up, the other goes down. If 6 workers take 10 days to dig a trench, the total work is 60 worker-days. So 12 workers take 5 days, and 4 workers take 15 days. Ask yourself: “More workers means more or less time?” If less, it is inverse.
Rates and Speed
A rate compares quantities of different kinds, such as kilometres per hour or shillings per kilogram. Speed = distance ÷ time.
- A matatu covers 150 km in 2 hours 30 minutes. Speed = 150 ÷ 2.5 = 60 km/h.
- At 80 km/h, how long does a 200 km journey take? 200 ÷ 80 = 2.5 hours, which is 2 hours 30 minutes.
- To change km/h to m/s, multiply by 1,000 and divide by 3,600. So 72 km/h = 20 m/s.
Best-Buy Problems
Compare the price per unit. A 500 g packet of tea costs KSh 260 and a 250 g packet costs KSh 140. The large packet is KSh 52 per 100 g and the small one KSh 56 per 100 g, so the large packet is better value.
Ratio and Map Scales
A map scale of 1:50,000 means 1 cm on the map is 50,000 cm, or 500 m, on the ground. A distance of 6 cm on the map is 3 km in reality. This links neatly with geography map work.
Common Mistakes
- Writing the ratio in the wrong order.
- Comparing quantities in different units.
- Treating inverse proportion as direct.
- Forgetting to convert minutes to hours when finding speed.
Keep Practising
Use everyday examples: recipes, fuel prices and journey times. Then practise exam questions using the exam countdown and track gaps with the What to Revise report. Our linear equations guide and the Grade 8 Mathematics papers are good next steps. Full timed papers with worked answers are in the Monthly Pass (KSh 500 by M-Pesa).