Last reviewed: 7 November 2026
Updated November 2026. These Grade 8 notes on rates, ratio, proportion and percentages cover working out rates, comparing and sharing ratios, increasing or decreasing a quantity in a ratio, percentage change, and direct and inverse proportion. Percentage change = (change ÷ original value) × 100.
All examples are original practice, not an official paper. For the other topics, see our Grade 8 mathematics revision guide.
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What the Grade 8 Curriculum Covers
Rates, ratio, proportions and percentages is a sub-strand under Numbers in the Kenya Institute of Curriculum Development’s Grade 8 Mathematics design. It includes rates, comparing ratios, increase and decrease of quantities, percentage change, and direct and indirect proportion. The design is listed on the KICD Grade Eight curriculum designs page.
Rates
A rate compares two different quantities, such as shillings per kilogram or litres per minute. A tap fills 120 litres in 8 minutes, so the rate is 120 ÷ 8 = 15 litres per minute.
Ratios: Simplifying, Comparing and Sharing
A ratio compares quantities of the same kind. Simplify by dividing by the highest common factor: 18 : 24 = 3 : 4.
Comparing. Which is greater, 3 : 4 or 5 : 7? Write as fractions with a common denominator: 3/4 = 21/28 and 5/7 = 20/28, so 3 : 4 is greater.
Sharing. Share KSh 1,200 in the ratio 2 : 3. Total parts = 5; one part = 240. Shares: KSh 480 and KSh 720.
Increase and Decrease Using a Ratio
To increase 60 in the ratio 5 : 4, multiply by 5/4: 60 × 5/4 = 75. To decrease 60 in the ratio 3 : 4, multiply by 3/4: 45. The first number of the ratio is the new value.
Percentage Change
Percentage change = (new − original) ÷ original × 100. A bag of flour rises from KSh 200 to KSh 230: change = 30, percentage increase = 30/200 × 100 = 15%. A class falls from 50 to 45 learners: decrease = 5/50 × 100 = 10%.
Direct and Inverse Proportion
Direct: both quantities rise together. If 4 books cost KSh 600, 1 book costs 150, so 7 books cost KSh 1,050.
Inverse (indirect): one rises as the other falls. If 6 workers take 10 days to dig a trench, the total work is 60 worker-days, so 4 workers take 60 ÷ 4 = 15 days.
Original Practice Questions With Worked Answers
- A car uses 24 litres of fuel for 300 km. Find the rate in km per litre.
Answer: 300 ÷ 24 = 12.5 km per litre. - Share 84 sweets in the ratio 3 : 4.
Answer: one part = 12; shares 36 and 48. - Increase 90 in the ratio 7 : 6.
Answer: 90 × 7/6 = 105. - A shirt price falls from KSh 800 to KSh 680. Find the percentage decrease.
Answer: 120/800 × 100 = 15%. - 8 taps fill a tank in 3 hours. How long would 6 taps take?
Answer: 24 tap-hours ÷ 6 = 4 hours.
Grade 9 builds on this in our Grade 9 compound proportions and rates of work notes.
For daily practice across subjects, a Day Pass (KSh 20) or Monthly Pass (KSh 500) opens the full question bank.
Frequently Asked Questions
What is the difference between a rate and a ratio?
A rate compares different kinds of quantities, such as km per litre. A ratio compares quantities of the same kind, such as boys to girls.
How do I calculate percentage change?
Divide the change by the original value and multiply by 100.
How do I know if proportion is direct or inverse?
If both quantities increase together, it is direct. If one increases while the other decreases, it is inverse.
How do I share an amount in a ratio?
Add the parts of the ratio, divide the amount by the total to find one part, then multiply by each part.
Ten-minute check: try the free Grade 8 CBC Challenge. It has 10 questions, each marked on the spot with the working, and it shows which topics to practise next.