The total-parts method
Sharing an amount in a ratio means splitting it into unequal portions according to the ratio given. The most reliable method works in three steps every time:
- Add up the total number of parts in the ratio.
- Divide the total amount by the total number of parts, to find the value of one part.
- Multiply the value of one part by each number in the ratio, to find each share.
Worked Example 1
Share £40 between Amy and Ben in the ratio 3:5.
1
Add the parts: 3 + 5 = 8 total parts
2
Find the value of one part: £40 ÷ 8 = £5
3
Multiply each part by £5: Amy = 3 × £5 = £15, and Ben = 5 × £5 = £25
AnswerAmy: £15, Ben: £25
The bar's total width represents the whole amount — its length is split into parts matching the ratio, so each part's size can be found and checked against the total.
Sharing in a three-part ratio
The same total-parts method works for ratios with three or more parts — just add up all the parts before dividing.
Worked Example 2
Share £180 between three friends in the ratio 2:3:4.
1
Add the parts: 2 + 3 + 4 = 9 total parts
2
Find the value of one part: £180 ÷ 9 = £20
3
Multiply each part by £20: 2 × £20 = £40, 3 × £20 = £60, 4 × £20 = £80
Answer£40, £60, £80
Working backwards from a share
Some questions give you the value of one share and ask you to find the total amount, or one of the other shares. Find the value of one part first, then scale up.
Worked Example 3
Two amounts are in the ratio 2:7. The smaller amount is £18. Find the total amount.
1
The smaller amount (2 parts) is £18, so one part is worth: £18 ÷ 2 = £9
2
Find the total number of parts: 2 + 7 = 9
3
Multiply the total parts by the value of one part: 9 × £9 = £81
Answer£81
Sharing using a difference between shares
Sometimes you're told the difference between two shares rather than one share directly. Use the difference in parts to find the value of one part.
Worked Example 4
Two amounts are in the ratio 3:5. The larger amount is £24 more than the smaller amount. Find both amounts.
1
Find the difference in parts: 5 − 3 = 2 parts
2
This difference is worth £24, so one part is worth: £24 ÷ 2 = £12
3
Find each amount: smaller = 3 × £12 = £36, larger = 5 × £12 = £60
Answer£36 and £60
Practice questions
Work through each question before checking the answers.
Foundation (Grade 3–5)
Q1Share £60 between Sam and Tia in the ratio 1:2.Foundation
Q2Share 50kg of flour between two bakeries in the ratio 2:3.Foundation
Q3Share £84 between three siblings in the ratio 1:2:4.Foundation
Q4A prize of £200 is shared in the ratio 3:2. How much is the larger share?Foundation
Q5Share 32 sweets between two friends in the ratio 3:5.Foundation
Higher (Grade 5–7)
Q6Two amounts are in the ratio 3:4. The smaller amount is £45. Find the total amount.Higher
Q7£450 is shared between three charities in the ratio 2:3:5. Find the amount each charity receives.Higher
Q8Two amounts are in the ratio 4:7. The larger amount is £30 more than the smaller amount. Find both amounts.Higher
Q9A recipe mixture is shared in the ratio 5:3. The larger part weighs 250g. Find the weight of the smaller part.Higher
Q10A sum of money is shared between Priya and Jo in the ratio 5:6. Priya receives £15 less than Jo. Find the total sum shared.Higher
Higher — Hard (Grade 8–9)
Q11£720 is shared between A, B and C. A gets twice as much as B, and B gets three times as much as C. Find the amount C receives.Grade 8–9
Q12Two amounts are in the ratio 2:9. If both amounts are increased by £12, the new ratio becomes 1:3. Find the original two amounts.Grade 8–9
Q13A sum of £600 is shared between X, Y and Z in the ratio 2:3:5. X then gives Y £20. Find the new ratio of X to Y, in its simplest form.Grade 8–9
Q14The ratio of red to blue counters in a bag is 3:8. There are 40 more blue counters than red counters. How many counters are there in total?Grade 8–9
Q15A total of £1,000 is shared between three people so that the second receives £40 more than the first, and the third receives twice as much as the second. Find all three amounts.Grade 8–9
Answers
Foundation (Q1–Q5)
Q1Sam: £20, Tia: £40
Q220kg and 30kg
Q3£12, £24, £48
Q4£120(£40 per part, 3 × £40)
Q512 and 20
Higher (Q6–Q10)
Q6£105(£15 per part, 7 parts total)
Q7£90, £135, £225
Q8£40 and £70(£10 per part, from the difference of 3 parts)
Q9150g(£50 per part, 3 × 50)
Q10£165(£15 per part, from the difference of 1 part, 11 parts total)
Higher — Hard (Q11–Q15)
Q11£72(ratio A:B:C = 6:3:1, 10 parts, £72 per part)
Q12£16 and £72((2x+12):(9x+12) = 1:3 → x = 8, so 2x=16, 9x=72)
Q131 : 2(X: £120 − £20 = £100, Y: £180 + £20 = £200, ratio 100:200 = 1:2)
Q1488 counters(difference of 5 parts = 40, so 1 part = 8, total 11 parts)
Q15£220, £260, £520(1st = x, 2nd = x+40, 3rd = 2(x+40); solve 4x+120=1000)
Common mistakes
Common Mistake 1
Dividing the amount by the wrong number
£40 shared in the ratio 3:5 is not divided by 3 or 5 alone — it must be divided by the total number of parts (3 + 5 = 8) to find the value of one part.
Common Mistake 2
Forgetting to check the shares add back up
After finding each share, always add them together and check they equal the original total — this catches most arithmetic slips immediately.
Common Mistake 3
Using the difference in amounts instead of the difference in parts
When a question gives a difference (e.g. "£24 more"), that £24 corresponds to the difference in ratio parts, not the value of a single part — divide by the difference in parts first.
Common Mistake 4
Mixing up which share is which
Always match each number in the ratio to the correct name or item in the order given — writing shares in the wrong order is a common way to lose easy marks.
Exam tips
💡 Exam Tip 1
Always find "one part" first
Whatever the question gives you — a total, one share, or a difference — the fastest route to the answer is almost always finding the value of a single part first.
💡 Exam Tip 2
Show your total-parts step clearly
Writing "total parts = ..." as a clear first line of working picks up method marks even if the final answer contains a small arithmetic error.
💡 Exam Tip 3
Watch out for "more than" and "less than" wording
Phrases like "£24 more than" signal a difference question, not a direct share — re-read the question carefully to decide which method applies.
💡 Exam Tip 4
Sense-check your final answer
Check the larger share in your answer actually corresponds to the larger number in the ratio — a common slip is accidentally swapping the two shares round.
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