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Level 6Grade 6skill: ratio_intro· 8 min read

Ratios Explained: Sharing in a Given Ratio

In short: To share an amount in a ratio, add the ratio numbers to get the total number of equal parts, divide the amount by that total to find the value of one part, then multiply each ratio number by one part. Always check that your shares add back up to the amount you started with.

How to share an amount in a given ratio

A ratio like 3:4 does not mean "3 things and 4 things". It means the amount is split into equal-sized parts, and one person gets 3 of those parts while the other gets 4. So the very first move is always the same: find out how many equal parts there are altogether.

Once you know the size of a single part, every share is just that one part counted the right number of times.

  1. Add the ratio numbers together to find the total number of equal parts.
  2. Divide the amount you are sharing by that total to find the value of ONE part.
  3. Multiply each ratio number by the value of one part to get each share.
  4. Check: add all the shares back up — they must equal the original amount.

Why this works (the one idea behind every ratio) Why it works

Add first
The ratio numbers are counts of equal parts, so the total number of parts is their sum, not the sum of the amounts.

3:4 is 7 equal parts — not 3 and 4 out of 10.

One part is the key
Divide the amount by the total parts to get the size of a single part. Every share is a multiple of that one number.

£56 ÷ 7 = £8 per part, so 3:4 becomes £24 : £32.

Scale, do not stop
Multiply each ratio number by one part — the ratio number tells you how many parts that share is worth.

4 parts × £8 = £32.

Here is the insight worth keeping: a ratio question is a division in disguise. The sum of the ratio numbers is a hidden denominator, and "one part" is the unit everything is built from. Find one part and every share, every difference, and every total falls straight out of it — you never need to guess.

Worked examples

Share £48 between two people in the ratio 5:3. = £30 and £18
  1. Add the parts: 5 + 3 = 8 parts.
  2. One part: £48 ÷ 8 = £6.
  3. Shares: 5 × £6 = £30 and 3 × £6 = £18.
  4. Check: £30 + £18 = £48.
Share 90 counters between three trays in the ratio 2:3:4. = 20, 30 and 40 counters
  1. Add the parts: 2 + 3 + 4 = 9 parts.
  2. One part: 90 ÷ 9 = 10 counters.
  3. Shares: 2 × 10 = 20, 3 × 10 = 30, 4 × 10 = 40.
  4. Check: 20 + 30 + 40 = 90.
A prize is shared between Mia and Tom in the ratio 7:2. Mia gets £45 more than Tom. What is the total prize? = £81
  1. This time you are told a difference, not the total. Use the difference in parts.
  2. Difference in parts: 7 − 2 = 5 parts, and those 5 parts are worth £45.
  3. One part: £45 ÷ 5 = £9.
  4. Total parts: 7 + 2 = 9, so total = 9 × £9 = £81 (Mia £63, Tom £18, difference £45).
Red and white paint are mixed in the ratio 2:5. You use 15 litres of white. How much red do you need? = 6 litres of red
  1. You are told the size of ONE colour, not the total. Match it to its parts.
  2. White is 5 parts, and that equals 15 litres, so one part = 15 ÷ 5 = 3 litres.
  3. Red is 2 parts: 2 × 3 = 6 litres.
Share 1.5 kg of flour in the ratio 4:1 and give the larger share in grams. = 1200 g
  1. Convert first so the units match the answer: 1.5 kg = 1500 g.
  2. Add the parts: 4 + 1 = 5 parts.
  3. One part: 1500 ÷ 5 = 300 g.
  4. Larger share: 4 × 300 = 1200 g.

Common mistakes

Splitting it in half instead of by the ratio

✗ £22.50 each

For "Share £45 in the ratio 4:5", it is tempting to just halve the money: £45 ÷ 2 = £22.50. But 4:5 is not an even split — it is 9 parts, not 2. Halving throws the ratio away completely.

Fix: Add the ratio numbers first (4 + 5 = 9), then divide by that total. One part is £45 ÷ 9 = £5, giving shares of £20 and £25.

wrong_operation

Finding one part and stopping there

✗ £5

In "Share £45 in the ratio 4:5", you correctly work out that one part is £45 ÷ 9 = £5 — then write £5 as the answer. But £5 is the size of a single part, not anyone's share.

Fix: Always scale. Multiply one part by each ratio number: 4 × £5 = £20 and 5 × £5 = £25. The check (£20 + £25 = £45) tells you the job is finished.

partial_computation

Dropping a zero in the division

✗ 15 cm

For "Share 240 cm in the ratio 5:3", one part should be 240 ÷ 8 = 30 cm. Rushing, you compute 24 ÷ 8 = 3 and lose the zero, then work out 5 × 3 = 15 cm. The ratio is right but the magnitude is ten times too small.

Fix: Keep the place value: 240 ÷ 8 = 30, not 3. That gives shares of 5 × 30 = 150 cm and 3 × 30 = 90 cm, which correctly add to 240 cm.

place_value_slip

Not converting the units before you share

✗ 1 g

For "Share 2 kg of sweets in the ratio 2:3:5, largest bag in grams", you share the number 2 as if it were grams: 2 ÷ 10 = 0.2, then 5 × 0.2 = 1, and write 1 g. You shared kilograms but labelled the answer grams.

Fix: Convert to the units the question asks for first: 2 kg = 2000 g. Then 2000 ÷ 10 = 200 g per part, so the largest bag is 5 × 200 = 1000 g.

unit_mismatch

Practice: sharing in a given ratio

This set mixes things up. Some questions give you the total to share, but others hand you the difference between two shares or the size of just one share instead. Read each one carefully and work out <em>which</em> quantity you have actually been given before you reach for one part.

Before and after this skill

First, make sure of

Frequently asked questions

What does a ratio like 3:2 actually mean?

It means the amount is split into equal parts, and for every 3 parts of the first thing there are 2 parts of the second. Together that is 5 equal parts — so 3:2 is not "3 out of 2" or "3 and 2 out of 10", it is 3 parts and 2 parts of the same-sized unit.

How is a ratio different from a fraction?

A fraction compares one part to the whole, while a ratio compares parts to each other. In the ratio 3:2 the first share is 3 out of every 5 parts, so as a fraction of the total it is 3/5. Turning the ratio numbers into fractions over the total (the sum of the parts) is often the quickest way to check your answer.

What do I do if the ratio has three numbers, like 2:3:5?

Exactly the same method. Add all three (2 + 3 + 5 = 10) to get the total parts, divide the amount by 10 to find one part, then multiply each number by that one-part value. The steps never change — there are just more shares to work out.

What if the amount doesn't divide evenly by the total number of parts?

At grade 6 the numbers are usually chosen so one part comes out whole. If you get a remainder, first double-check your total number of parts and your division. Genuine cases (like sharing money) can give decimals, e.g. £45 in the ratio 4:5 gives £5 a part exactly, but £10 in the ratio 1:2 gives £3.33 and £6.67 — round money to the nearest penny only at the very end.

How can I check my ratio answer is right?

Two quick checks. First, add all your shares together — they must equal the original amount. Second, the shares should be in the same ratio you started with: 24:32 divides down to 3:4, which matches. If both checks pass, your answer is correct.