This mini-lesson covers the whole Ratio, Proportion & Rates of Change strand of Eduqas GCSE Maths: sharing in a ratio, direct & inverse proportion, percentages & compound interest, and rates such as speed, density & pressure, plus growth & decay.
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 divide a quantity in a ratio, add the parts to find the total number of parts, then find one part:
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 ✓)
Ratio ⇄ fraction: in the ratio 5 : 3 the first share is 5⁄8 of the total, not 5⁄3. The denominator is the total number of parts. Always check your shares add back to the original total.
Two quantities are in direct proportion when one is a fixed multiple of the other — double one and you double the other. Use the unitary method: find the value of one, then scale up.
5 pens cost £3.50. How much do 8 pens cost?
One pen: 3.50 ÷ 5 = £0.70
Eight pens: 0.70 × 8 = £5.60
Tip: "y is directly proportional to x" means y = kx, so a graph of y against x is a straight line through the origin. As x goes up, y goes up.
Two quantities are in inverse proportion when one increases as the other decreases, keeping their product constant. Think "more workers → fewer days".
3 taps fill a tank in 40 minutes. How long for 5 taps (same rate)?
Total "tap-minutes" = 3 × 40 = 120 (constant)
With 5 taps: 120 ÷ 5 = 24 minutes
Don't just scale up: inverse proportion is not "5 taps take 5⁄3 × 40". Find the constant product first (3 × 40 = 120), then divide.
Every percentage change has a single multiplier. Tap a change on the left, then its matching multiplier on the right.
Percentage means "parts per 100". The quickest way to increase or decrease is a single multiplier:
A £40 coat is reduced by 30%. New price?
Multiplier for a 30% decrease = 1 − 0.30 = 0.70
40 × 0.70 = £28
When you're given the final amount and asked for the original, work backwards: divide by the multiplier.
A sofa costs £360 after a 20% discount. Find the original price.
£360 is 80% of the original → multiplier = 0.80
original = 360 ÷ 0.80 = £450
The classic trap: reverse percentage is not "just add the 20% back". Adding 20% to £360 gives £432, which is wrong. You must divide by 0.80 to undo the discount.
With compound interest the change is applied repeatedly, each year 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.)
Decay / depreciation works the same way but with a decrease multiplier — e.g. a car losing 15% of its value each year uses ×0.85 raised to the power of the number of years.
A rate compares one quantity to another, giving a compound unit like km/h or m/s. Speed is distance per unit time:
A train travels 210 km in 3 hours. Find its average speed.
speed = 210 ÷ 3 = 70 km/h
Density is another rate — mass per unit volume, measured in units like g/cm³. It uses the same triangle idea as speed:
A block has mass 480 g and volume 60 cm³. Find its density.
density = 480 ÷ 60 = 8 g/cm³
Watch the units: mass in grams and volume in cm³ give g/cm³. If mass were in kg and volume in m³ the density would be in kg/m³ — always keep units consistent.
Pressure is force spread over an area, measured in newtons per square metre (N/m², also called pascals). Same triangle structure again:
A force of 60 N acts on an area of 3 m². Find the pressure.
pressure = 60 ÷ 3 = 20 N/m²
Same family: speed, density and pressure are all "one thing ÷ another thing" rates. Master one triangle and you can rearrange all three.
In direct proportion both quantities grow together; in inverse proportion one grows as the other shrinks. Tap a relationship, then tap the box it belongs in.
Ratio: add the parts, find one part, multiply up; the ratio a : b makes a fraction a⁄(a+b) of the whole.
Direct proportion: y = kx, straight line through the origin; unitary method — find one, then scale.
Inverse proportion: x × y = k stays constant; more of one means less of the other.
Percentages: multipliers; +15% → ×1.15; reverse percentage = ÷ multiplier.
Compound interest, growth & decay: amount = P × (multiplier)ⁿ.
Rates: speed = distance ÷ time, density = mass ÷ volume, pressure = force ÷ area — one triangle rearranges all three.
You've covered every part of the Ratio, Proportion & Rates of Change strand of Eduqas GCSE Maths. Press Finish to see your score.
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