Ratio, Proportion & Rates of Change
Grade 4-5Sharing in a Given Ratio
Sharing an amount in a ratio always starts the same way, by finding the value of a single part, and every other quantity in the problem, whether it is a share, a difference or a total, is built from that one value. This lesson covers sharing an amount in a two-part or three-part ratio, working backwards to find the total when only one share is known, and finding the difference between shares.
What you need to know
- Add the ratio parts to find the total number of shares.
- Divide the amount by the total shares to find what one share is worth.
- Multiply one share by each part of the ratio.
- Check that your amounts add back up to the original total.
Written by Asad, co-founder of Teachably
Video walkthrough coming soon
The written lesson below covers everything you need in the meantime.
Sharing an amount in a two-part ratio
Add the parts of the ratio together to find the total number of parts, divide the amount by this total to find the value of one part, then multiply that value by each number in the ratio to find each share.
Share £60 in the ratio 2:3: the total number of parts is 2 + 3 = 5, so one part is £60 ÷ 5 = £12. The shares are 2 × £12 = £24 and 3 × £12 = £36.
Sharing an amount in a three-part ratio
The same method extends to three (or more) parts: add all the parts together, divide the amount by the total, then multiply back for each share.
Share £120 in the ratio 1:2:3: the total number of parts is 1 + 2 + 3 = 6, so one part is £120 ÷ 6 = £20. The shares are £20, £40 and £60.
Working backwards to find the total
If one share is known instead of the whole amount, divide that share by its own number of parts to find the value of one part, then multiply by the total number of parts in the ratio to find the whole amount.
Amy and Zoe share money in the ratio 2:7, and Amy receives £16. One part is £16 ÷ 2 = £8, so the total shared is (2 + 7) × £8 = £72.
Finding the difference between shares
Once each individual share has been found, the difference between two shares is simply found by subtracting the smaller share from the larger one.
Share £280 in the ratio 3:4: one part is £280 ÷ 7 = £40, giving shares of £120 and £160. The difference between the shares is £160 - £120 = £40.
Worked examples
Three exam-style questions, fully solved
Share £60 in the ratio 2:3.
Easy- 1.Find the total number of parts: 2 + 3 = 5
- 2.Find the value of one part: £60 ÷ 5 = £12
- 3.Multiply by each number in the ratio: 2 × £12 and 3 × £12
Answer: £24 : £36
Share £280 in the ratio 3:4. Find the difference between the two shares.
Medium- 1.Find the total number of parts: 3 + 4 = 7
- 2.Find the value of one part: £280 ÷ 7 = £40
- 3.Find the two shares: 3 × £40 = £120, and 4 × £40 = £160
Answer: £40
The angles in a triangle are in the ratio 2:3:4. Find the size of the largest angle.
Hard- 1.Find the total number of parts: 2 + 3 + 4 = 9
- 2.Recognise that the angles in a triangle sum to 180°, so this is the total to share
- 3.Find the value of one part: 180° ÷ 9 = 20°
- 4.Find the largest angle: 4 × 20°
Answer: 80°
Practice
6 questions, marked instantly
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Practice
Now try these yourself.
Type your answer and check it. The worked solution appears once you have had a go.
Share £40 in the ratio 3 : 5.
Share 24 sweets in the ratio 1 : 3.
Divide 100 in the ratio 2 : 3 : 5.
Two people share money in the ratio 4 : 7. The larger share is £63. Work out the smaller share.
A drink is made from squash and water in the ratio 1 : 6. How much water is needed to make 350 ml of the drink?
In a bag, the ratio of red to blue counters is 2 : 5. There are 20 red counters. How many counters are in the bag altogether?
Avoid these
The mistakes students make most often
Dividing the amount by the number of shares (for example by 2) instead of by the total number of parts in the ratio.
Finding the value of one part but forgetting to multiply it back by each ratio number to find the individual shares.
When working backwards from one known share, dividing by the wrong number of parts.
Not recognising that a real-world total, such as the angles of a triangle summing to 180°, needs to be identified before it can be used as the amount to share.
Giving the value of one part as the final answer instead of completing the calculation for the actual quantity the question asked for.
FAQ
Questions students and parents ask
Before this topic, make sure you know
What to learn next
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