Ratio & Proportion
Sharing in a ratio, direct and inverse proportion.
Watch the lesson
Every point below, worked through in one video, and each point links straight to its own part.
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Ratio & Proportion, explained point by point
Everything the GCSE specification expects you to be able to do, and how to actually do it - the same lesson a signed-in student studies from.
Write and simplify ratios, including in the form 1 : n
Ratios simplify like fractions - divide every part by the same number: 12 : 18 = 2 : 3. Units must match before you simplify (50p : £2 is 50 : 200 = 1 : 4). For the form 1 : n, divide both sides by the first number, even if n comes out as a decimal.
Divide a quantity in a given ratio
Add the parts, divide the total by that sum to find one part's worth, then multiply up. Sharing £60 in the ratio 2 : 3 : 5 means 10 parts, so one part is £6, giving £12, £18 and £30. Check the shares add back to the total.
Solve ratio problems where one part, or the difference between parts, is known
Work out what one part is worth from the clue you have. If money is shared 3 : 5 and the LARGER share is £40, then 5 parts = £40, so one part is £8 and the other share is £24. If the DIFFERENCE is £16, then the 2-part gap equals £16 and one part is £8 again.
Move between ratios and fractions of a whole
A ratio of 2 : 3 means the whole has 5 parts - so the first quantity is of the total, not . Going the other way, " of the class are boys" means boys : girls = 3 : 4. Keep asking: parts of WHAT whole?
Use scale factors, scale diagrams and maps
A scale of 1 : 25 000 means 1 cm on the map is 25 000 cm - 250 m - in real life. Multiply by the scale to go from map to world, divide to come back. Keep an eye on units: convert cm to m or km at the end, not midway.
Compare value for money and convert between currencies
Find the price of ONE unit of each option and compare: 400 g for £2.40 is 0.6p per gram, 250 g for £1.60 is 0.64p - the first is better value. Currency conversion is the same idea: multiply by the rate one way, divide coming back.
Common mistakes in Ratio & Proportion
The slips that cost marks year after year, and what to do instead.
Dividing the total by each number in the ratio, so sharing £60 in the ratio 2 : 3 gives £30 and £20.
Add the parts first: 2 + 3 = 5 parts, so one part is 60 ÷ 5 = £12, giving £24 and £36. The shares should add back to £60.
Turning the ratio 2 : 3 into the fraction of the whole.
A ratio of 2 : 3 splits the whole into 5 parts, so the first share is of the total and the second is .
Treating a known share as the total: if the larger share in 3 : 5 is £40, dividing £40 into 8 parts.
Match the clue to its parts: 5 parts are worth £40, so 1 part is £8 and the smaller share is 3 × £8 = £24.
Simplifying before the units match, so 50p : £2 turns into 25 : 1.
Write both in the same units first: 50p : £2 is 50 : 200, which simplifies to 1 : 4.
Stopping at whole numbers when the question asks for the form 1 : n, so 4 : 10 is left as 2 : 5.
Divide both sides by the first number, even if n ends up as a decimal: 4 : 10 = 1 : 2.5.
Practice
Try a Ratio & Proportion question
A GCSE-style original question from this topic. Have a go before you open the working - deciding on an answer first is what makes the working stick.
Answer: £88
The £24 difference matches the difference in ratio parts (7 − 4 = 3), which lets you value one part and then the whole.
- Difference in parts = 7 − 4 = 3.
- 3 parts are worth £24, so one part = 24 ÷ 3 = £8.
- Total parts = 7 + 4 = 11.
- Total money = 11 × £8 = £88.
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