Functional Skills Maths · England

Ratio and proportion

Share amounts in a given ratio, scale recipes and mixes up or down, find the best buy, and — at Level 2 — handle inverse proportion, where more of one thing means less of another.

Audience
Adults & apprentices
Levels
Level 1 · Level 2 (inverse proportion)
Worked examples
4
Format
Print (A4/Letter) + answers

Learn

What a ratio tells you

A ratio compares the sizes of parts. A mortar mix of cement to sand of 1:4 means one bucket of cement for every four buckets of sand. The order matters: 1:4 is not the same as 4:1. Ratios can be simplified like fractions by dividing every part by the same number, so 12:18 becomes 2:3 when you divide both by 6.

Sharing in a ratio

To share an amount in a ratio, follow three steps. Add the parts to find the total number of parts. Divide the amount by that total to find the value of one part. Multiply by each part of the ratio. To share £180 in the ratio 2:3, there are 5 parts, one part is £36, and the shares are £72 and £108. Check by adding the shares — they should make the original amount.

Sometimes you are told the difference between shares instead of the total. If Sam and Tom split money 3:2 and Sam gets £240 more, the difference is one part, so one part is £240 and the total is five parts, £1,200.

Direct proportion and best buys

Two quantities are in direct proportion when they increase at the same rate: double the people, double the pasta. The most reliable approach is the unitary method — find the value for one, then multiply up. If a recipe for 4 people uses 300 g of pasta, that is 75 g per person, so 10 people need 750 g.

Best-buy questions compare different pack sizes. Work out the price for the same amount of each — per 100 g, per litre or per item — and compare. Convert to the same units first: 1.2 kg is 1,200 g. The pack with the lower price per unit is better value, although in real life you might still choose the smaller pack if you would waste the rest.

Exchange rates are another kind of direct proportion. If £1 buys €1.16, multiply pounds by 1.16 to get euros, and divide euros by 1.16 to get pounds.

Inverse proportion (Level 2)

In inverse proportion, as one quantity goes up the other goes down. More decorators finish a job faster; more guests make the food last fewer days. The amount of work stays the same, so multiply to find the total, then divide. If 6 decorators take 4 days, the job is 6 × 4 = 24 decorator-days, so 8 decorators take 24 ÷ 8 = 3 days. Ask yourself whether your answer should be bigger or smaller — it is an easy way to spot a direct-proportion slip.

At Level 1 you will typically simplify ratios, share in a ratio, scale recipes and compare simple best buys. Level 2 adds inverse proportion, three-part ratios and harder multi-step problems.

Worked example 1

Level 1: Share £180 between two people in the ratio 2:3.

  1. Total parts: 2 + 3 = 5.
  2. One part: £180 ÷ 5 = £36.
  3. Shares: 2 × £36 = £72 and 3 × £36 = £108.
  4. Check: £72 + £108 = £180.

Answer: £72 and £108

Worked example 2

Level 1: A recipe for 4 people uses 300 g of pasta. How much is needed for 10 people?

  1. One person: 300 ÷ 4 = 75 g.
  2. Ten people: 75 × 10 = 750 g.

Answer: 750 g

Worked example 3

Level 2: Rice costs £2.85 for 750 g or £4.32 for 1.2 kg. Which is better value?

  1. Use price per 100 g. 750 g is 7.5 lots of 100 g: £2.85 ÷ 7.5 = £0.38.
  2. 1.2 kg = 1,200 g = 12 lots of 100 g: £4.32 ÷ 12 = £0.36.
  3. 36p is less than 38p.

Answer: The 1.2 kg bag is better value (£0.36 per 100 g).

Worked example 4

Level 2: Six decorators take 4 days to paint a school. How long would 8 decorators take?

  1. This is inverse proportion: more people, fewer days.
  2. Total work: 6 × 4 = 24 decorator-days.
  3. 8 decorators: 24 ÷ 8 = 3 days.

Answer: 3 days

Watch out

Common mistakes

  • Dividing by one part of the ratio instead of the total number of parts.
  • Mixing up the order: in 2:3 the first person gets the smaller share.
  • Comparing best buys without converting to the same units (grams and kilograms, millilitres and litres).
  • Treating inverse proportion as direct: if more workers seem to take longer, the method is the wrong way round.

Real life

Where you'll use this at work or home

  • Kitchens: scaling a recipe from 4 portions to 30 for an event.
  • Building and DIY: mixing concrete, mortar, plaster or two-part paints in the right proportions.
  • Shopping: checking the price per 100 g on shelf labels to find real value.
  • Workplace planning: estimating how long a job will take with more or fewer staff, or splitting tips fairly.

Try it

Practice sheet

Functional Skills Maths · Level 1

Ratio and proportion

NameDate

Show your working. Give money to the nearest penny and include units in every answer.

  1. 1.Concrete is mixed cement to sand in the ratio 1:3. A builder uses 12 buckets in total. How many buckets of cement?
  2. 2.£240 of tips is shared between two staff in the ratio 3:5. How much is the larger share?
  3. 3.5 pens cost £3.50. How much do 8 pens cost?
  4. 4.Simplify the ratio 12:18.
  5. 5.Squash is mixed concentrate to water 1:4. How much water goes with 250 ml of concentrate?
  6. 6.A chilli for 6 people uses 450 g of mince. How much mince is needed for 4 people?
  7. 7.A car uses 6 litres of fuel per 100 km. How much fuel does it use on a 240 km trip?
  8. 8.Kai earns £84 for 7 hours' work. How much does he earn for 10 hours?
  9. 9.A school trip needs adults to children in the ratio 1:6. How many adults are needed for 42 children?
  10. 10.Cola is £2.40 for 4 cans or £3.30 for 6 cans. Which is better value?
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Questions

Frequently asked questions

Ask what happens when one quantity doubles. If the other doubles too, it is direct. If the other halves, it is inverse.

Only when the question asks, but simplifying often makes the numbers easier to work with. Divide every part by the same number.

Any unit works as long as you use the same one for every option. Price per 100 g or per litre is common because it matches shop shelf labels.

The method is identical: add all three parts, find one part, then multiply. Only the adding step has an extra number.

Next steps

Fractions, decimals and percentagesConvert, order, and find fractions and percentages of amounts.Units, time and conversionsMetric units, time, imperial conversions, speed and density.Scale drawings, maps and coordinatesMap scales, plans and elevations, and coordinates.All Functional Skills Maths topicsThe full learning path, Level 1 and Level 2.

Last reviewed: 9 October 2026

Editor: Paul Smeaton CMgr FCMI