Sharing in a Given Ratio
Sharing an amount in a given ratio means splitting it into parts that keep a fixed proportion between the groups, rather than splitting it equally: a total shared in the ratio a : b is cut into (a + b) equal-sized parts, with one group taking a of those parts and the other taking b. The key skill is finding the value of a single part first, then scaling it up by each number in the ratio, whether money, a mass, a length, or a number of objects is being shared.
Method
- Add together every number in the ratio to find the total number of parts.
- Divide the total amount being shared by the total number of parts. This gives the value of one part.
- Multiply the value of one part by each number in the ratio, in turn, to find every individual share.
- Add the shares back together as a check - they must equal the original total amount exactly.
- For a three-part ratio (or more), use exactly the same method: add all the numbers in the ratio first, then find the value of one part, then scale up each share.
- Give each share in the same unit as the original amount (pounds, grams, minutes, and so on), rounding only at the very end if the question asks for a rounded answer.
- If the question only asks for one of the shares, still find the value of one part first - it is usually the quickest route to any single share.
Worked example
A youth theatre group is given a grant of 456 pounds to split between its costume budget and its set-building budget in the ratio 5 : 7. Work out how much each budget receives.
- Add the parts of the ratio: 5 + 7 = 12 parts in total.
- Divide the grant by the total number of parts: 456 / 12 = 38 pounds per part.
- Costume budget = 5 x 38 = 190 pounds.
- Set-building budget = 7 x 38 = 266 pounds.
- Check: 190 + 266 = 456 pounds, which matches the original grant.
Practice questions
Type your answer and press Check to be marked straight away, or reveal the answer and mark yourself.
Q1Share 245 kg of sand between two building sites in the ratio 2 : 5.Show answer
Answer: 70 kg and 175 kg (245 / 7 = 35 kg per part, then 2 x 35 and 5 x 35)
Q2A cafe splits its weekly tips of 168 pounds between the kitchen staff and the front-of-house staff in the ratio 3 : 4. How much does the front-of-house team receive?Show answer
Answer: 96 pounds (168 / 7 = 24 pounds per part, then 4 x 24)
Q3A 600 g bag of trail mix is made from raisins, nuts and seeds in the ratio 2 : 3 : 5. Work out the mass of each ingredient in the mix.Show answer
Answer: Raisins = 120 g, nuts = 180 g, seeds = 300 g (600 / 10 = 60 g per part)
Q4Three cousins, Deepa, Marcus and Aoife, invest in a market stall and agree to share any profit in the ratio 4 : 5 : 6. The stall makes a profit of 300 pounds. How much does Marcus receive?Show answer
Answer: 100 pounds (300 / 15 = 20 pounds per part, then 5 x 20)
Q5A recipe for bread rolls uses flour and water in the ratio 8 : 3 by mass. If 660 g of dough is made in total, work out the mass of flour used.Show answer
Answer: 480 g (660 / 11 = 60 g per part, then 8 x 60)
Q6A charity shop sorts a delivery of 189 books into fiction and non-fiction in the ratio 5 : 4. Work out how many fiction books there are.Show answer
Answer: 105 books (189 / 9 = 21 books per part, then 5 x 21)
Q7A vet mixes 250 ml of medicine from two ingredients in the ratio 2 : 3. Work out the volume of the smaller ingredient used.Show answer
Answer: 100 ml (250 / 5 = 50 ml per part, then 2 x 50)
Exam-style questions
Written in the style of a KS3 Maths exam paper, with a full mark scheme.
A youth orchestra receives a donation of 1020 pounds to share between its string section fund and wind section fund in the ratio 7 : 8. The wind section then spends 96 pounds of its share on new reeds. Work out how much money the wind section has left.
Show mark scheme
Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 4 available
A bakery's flour delivery of 88 kg is shared between its main kitchen and its bread kitchen in the ratio 3 : 8. The bread kitchen then uses 40% of its share to bake a large batch of sourdough loaves. Work out how many kilograms of flour the bread kitchen has left after baking the sourdough loaves.
Show mark scheme
Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 5 available
Free printable worksheet
Want more practice on paper? Download the sharing in a given ratio worksheet pack - 6 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
This topic is chapter 36 of KS3 Maths Workbook 1, the whole course as one free printable PDF.
Next topics
Not quite what you needed?
Tell us what is missing on sharing in a given ratio, or which topic to write up next. Every request is read, and we reply to every one.
Build a full practice pack.
This topic is one of hundreds in the library - pick the ones a student needs and generate a printable PDF in minutes.