How to Share an Amount in a Given Ratio: KS3 Maths

To share an amount in a ratio, add the ratio parts to find the total number of shares, divide the amount by that total to find one share, then multiply by each ratio part. Always check by adding your answers — they must total the original amount.

What does sharing in a ratio mean?

A ratio tells you the relative sizes of each person's share. The ratio 2 : 3 does not mean one person gets 2 and another gets 3 — it means for every 2 units the first person receives, the second receives 3. The actual amounts depend on the total being shared.

Ratio | Total parts | Fraction for each share
1 : 4 | 5 | 1/5 and 4/5
2 : 3 | 5 | 2/5 and 3/5
3 : 5 | 8 | 3/8 and 5/8
1 : 2 : 3 | 6 | 1/6, 2/6, 3/6

What is the step-by-step method?

Follow three clear steps every time:

Add the ratio parts to find the total number of shares.

Divide the total amount by the number of shares to find the value of one share.

Multiply the value of one share by each ratio part to find each person's amount.

Then verify: add the shares together — they must equal the original total.

Worked example: sharing between two people

Share £40 in the ratio 3 : 5.

Total parts: 3 + 5 = 8

Value of one part: £40 ÷ 8 = £5

First share: 3 × £5 = £15; second share: 5 × £5 = £25

Check: £15 + £25 = £40 ✓

The two shares are £15 and £25.

Worked example: sharing between three people

Three friends share prize money of £120 in the ratio 1 : 2 : 3.

Total parts: 1 + 2 + 3 = 6

Value of one part: £120 ÷ 6 = £20

First: 1 × £20 = £20; second: 2 × £20 = £40; third: 3 × £20 = £60

Check: £20 + £40 + £60 = £120 ✓

The shares are £20, £40, and £60.

How do you find the original total from one person's share?

Sometimes you are given one person's share and asked to find the other's or the original total. Work backwards:

Example: Alice and Ben share money in the ratio 3 : 7. Alice receives £24. How much does Ben receive?

Alice's share = 3 parts = £24, so one part = £24 ÷ 3 = £8.

Ben's share = 7 parts = 7 × £8 = £56.

Original total = £24 + £56 = £80.

Ben receives £56 and the original total was £80.

How do you simplify a ratio first?

If the ratio contains large or awkward numbers, simplify it first by dividing all parts by their highest common factor (HCF).

Ratio 12 : 18 → HCF is 6 → simplified ratio is 2 : 3.

Ratio 15 : 10 : 5 → HCF is 5 → simplified ratio is 3 : 2 : 1.

Simplifying makes the arithmetic easier without changing the proportions.

What mistakes do students commonly make?

Adding the ratio parts incorrectly. In 3 : 5, the total is 8, not 5. Always add all the parts.

Forgetting to check. The check (shares add up to the total) takes five seconds and catches errors every time.

Treating the ratio numbers as the actual shares. A ratio 3 : 5 tells you the proportion, not the amounts. Without the total, you cannot find the actual shares.

Not simplifying. If you start with 6 : 10 and the total is £160, dividing by 16 parts is harder than simplifying to 3 : 5 and dividing by 8 parts.

Frequently asked questions

How do you share £360 in the ratio 2 : 7?

Total parts: 2 + 7 = 9. One part: £360 ÷ 9 = £40. First share: 2 × £40 = £80. Second share: 7 × £40 = £280. Check: £80 + £280 = £360. ✓

What if the ratio has decimals or fractions?

Multiply all parts by a suitable number to make them whole numbers. For example, ratio 0.5 : 1.5 becomes 1 : 3 after multiplying by 2. Then proceed with the standard method.

How do you find the total if you only know one share?

Divide the known share by its ratio part to find the value of one part. Then multiply one part by the sum of all ratio parts to find the total. For example, if the larger share in a 2 : 5 ratio is £35, one part = £35 ÷ 5 = £7, so total = 7 × £7 = £49.

Can a ratio question involve units other than money?

Yes — ratios appear with any quantity: lengths (e.g. mix concrete in 1 : 2 : 4 of cement : sand : gravel), masses, volumes, and more. The method is identical regardless of the unit: find one part, then multiply.

For Socratic ratio and proportion practice at KS3, see aitutors.me.