Appears in: Functional Skills Level 1 · Functional Skills Level 2 · GCSE foundation
Ratio and proportion: how to simplify, share in a ratio and scale up
Ratio questions look different on the surface — sharing money, mixing paint, scaling a recipe — but nearly all of them come down to one idea: find the value of one part. Once you have that, everything else is multiplying.
The method
- To simplify a ratio, divide every number in it by the same thing until you can't any more. 12 : 18 → divide both by 6 → 2 : 3.
- To share an amount in a ratio: add the ratio numbers to get the total parts, divide the amount by the total parts to get one part, then multiply by each ratio number.
- If you're told the difference between the shares rather than the total, the difference in the ratio numbers tells you how many parts that difference is worth.
- Direct proportion: find the value of one unit first (the unitary method), then multiply up.
Worked examples
Example 1
Share £350 between Ali and Sam in the ratio 2 : 5. How much does Sam get?
- Total parts: 2 + 5 = 7.
- One part: £350 ÷ 7 = £50.
- Sam gets 5 parts: 5 × £50 = £250. (Ali gets £100. Check: £100 + £250 = £350.)
Example 2
Two people share a bonus in the ratio 3 : 7. The larger share is £48 more than the smaller. What is the larger share?
- The difference in parts is 7 − 3 = 4 parts, and that's worth £48.
- One part: £48 ÷ 4 = £12.
- Larger share: 7 × £12 = £84. (Smaller: £36. Check: £84 − £36 = £48.)
Example 3
5 pens cost £3.20. How much do 8 pens cost?
- One pen: £3.20 ÷ 5 = £0.64.
- 8 pens: 8 × £0.64 = £5.12.
Example 4
A recipe for 4 people uses 300 g of rice. How much rice for 10 people?
- Per person: 300 ÷ 4 = 75 g.
- For 10: 75 × 10 = 750 g.
Where the marks go missing
- Dividing the total by the number of people instead of by the number of parts. In 2 : 5, there are 7 parts, not 2.
- Giving the smaller share when the question asks for the larger one, or the other way round — read which one it wants.
- Simplifying only one side of a ratio. Whatever you divide by, divide every number by it.
Frequently asked questions
How do you share an amount in a ratio?
Add the ratio numbers to get the total number of parts, divide the amount by that to find one part, then multiply one part by each ratio number. £120 in 1 : 3 is 4 parts of £30, so £30 and £90.
What is the unitary method?
Find the value of one unit first, then scale. If 6 items cost £9, one costs £1.50, so 10 cost £15.