This mini-lesson covers the whole Ratio, Proportion & Rates of Change strand of Edexcel GCSE Maths (1MA1): sharing & simplifying ratio, direct & inverse proportion, percentage change, compound interest & depreciation, growth & decay, and the compound measures — speed, density and pressure.
Work through each screen, answer the questions as you go (some are wordy, most are calculations) and collect ⭐ stars. Press Start when you're ready.
To simplify a ratio, divide every part by their highest common factor. To share a quantity in a ratio, add the parts to get the total number of parts, then find one part:
Simplify 12 : 18. The HCF of 12 and 18 is 6.
12 ÷ 6 = 2 and 18 ÷ 6 = 3 → 2 : 3
Share £416 in the ratio 5 : 3.
Total parts = 5 + 3 = 8, so one part = 416 ÷ 8 = £52
Shares: 5 × 52 = £260 and 3 × 52 = £156 (check: 260 + 156 = 416 ✓)
Always check your shares add back to the original total — a quick way to catch arithmetic slips.
Speed is a compound measure — a rate that combines two quantities. Speed, distance and time are linked by one triangle:
A train travels 180 km in 3 hours. Average speed?
speed = distance ÷ time = 180 ÷ 3 = 60 km/h
Watch the units: a time of 2 hours 30 minutes is 2.5 hours, not 2.30. Convert minutes to a decimal fraction of an hour first.
Density is how much mass is packed into a given volume — another compound measure with its own triangle:
A block has mass 500 g and volume 100 cm³. Density?
density = mass ÷ volume = 500 ÷ 100 = 5 g/cm³
Units matter: density in g/cm³ needs mass in grams and volume in cm³. Mixing kg with cm³ gives a wrong answer.
Percentage means "parts per 100". The quickest way to increase or decrease is a multiplier:
A £40 coat is reduced by 30%. New price?
Multiplier for a 30% decrease = 1 − 0.30 = 0.70
40 × 0.70 = £28
Percentage change = (change ÷ original) × 100. Always divide by the original amount, not the new one.
With compound change the same percentage is applied repeatedly, each period on the new total. Use the multiplier raised to a power:
£1000 invested at 5% compound interest for 3 years.
Multiplier = 1.05 → 1000 × 1.05³
1.05³ = 1.157625 → £1157.63 (2 d.p.)
A car worth £8000 depreciates 10% per year for 2 years.
Multiplier = 0.90 → 8000 × 0.90² = 8000 × 0.81 = £6480
Growth vs decay: growth uses a multiplier above 1 (×1.05); decay/depreciation uses one below 1 (×0.90). Both are raised to the power n.
Tap a ratio on the left, then its fully simplified form on the right.
In direct proportion two quantities rise together: y = kx. In inverse proportion, as one goes up the other goes down, and their product stays constant:
y is inversely proportional to x. When x = 2, y = 15.
k = x × y = 2 × 15 = 30
When x = 5: y = 30 ÷ 5 = 6
Direct vs inverse: in direct proportion you divide to find k (k = y ÷ x); in inverse proportion you multiply to find k (k = x × y).
Pressure is the force pushing on each unit of area — the third compound measure. It uses the same triangle idea:
A force of 60 N acts on an area of 3 m². Pressure?
pressure = force ÷ area = 60 ÷ 3 = 20 Pa
Same shape, different letters: speed/distance/time, mass/density/volume and force/pressure/area all follow the identical triangle — learn one, learn all three.
A multiplier above 1 increases an amount; a multiplier below 1 decreases it. Tap a multiplier, then tap the box it belongs in.
Ratio: simplify by dividing by the HCF; share by finding one part = total ÷ (sum of parts).
Proportion: direct → y = kx (k = y ÷ x); inverse → y = k ÷ x (k = x × y).
Percentages: use multipliers; increase → ×(1 + %), decrease → ×(1 − %); % change ÷ original.
Compound interest & depreciation: amount = P × (multiplier)ⁿ — growth ×>1, decay ×<1.
Speed: speed = distance ÷ time (watch the time units).
Density: density = mass ÷ volume, so mass = density × volume.
Pressure: pressure = force ÷ area (Pa = N/m²).
Same triangle works for speed, density and pressure alike.
You've covered every part of the Ratio, Proportion & Rates of Change strand of Edexcel 1MA1. Press Finish to see your score.
You've worked through Ratio, Proportion & Rates of Change for Edexcel GCSE Maths. 🎉
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Next: test yourself in the Evaluate stage Confidence Quiz, then lock it in with Verify.