ZIMSEC O Level · Mathematics · Form 1, Form 2
A ratio compares two or more quantities of the same kind. Simplify a ratio by dividing all parts by their HCF: 12 : 18 = 2 : 3.
Sharing in a given ratio
Add the parts, find the value of one part, then multiply.
Worked example: Share US$450 between Tendai and Nkosi in the ratio 4 : 5.
Total parts = 4 + 5 = 9. One part = 450 ÷ 9 = 50.
Tendai: 4 × 50 = US$200. Nkosi: 5 × 50 = US$250.
Rates
A rate compares quantities of different kinds, e.g. km per hour or dollars per kilogram.
- Speed = distance ÷ time.
- Change units carefully: 1 hour = 60 minutes; 1 km = 1000 m.
Worked example: A bus travels 180 km in 2 hours 30 minutes. Find its average speed.
2 hours 30 minutes = 2.5 hours
Speed = 180 ÷ 2.5 = 72 km/h
Direct and inverse proportion
- Direct: when one quantity doubles, the other doubles (cost of 5 pens vs 10 pens).
- Inverse: when one quantity doubles, the other halves (more workers, fewer days).
Worked example: 6 workers build a wall in 10 days. How long would 4 workers take?
Total work = 6 × 10 = 60 worker-days. 60 ÷ 4 = 15 days.
Check yourself
- Simplify 250 g : 2 kg.
- A car uses 8 litres of fuel to travel 100 km. How much fuel is needed for 340 km?
- A map scale is 1 : 50 000. Two towns are 7 cm apart on the map. Find the real distance in km.
Show answers
- 250 : 2000 = 1 : 8
- 27.2 litres
- 350 000 cm = 3.5 km
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