# Unit 7 Section 3 : Proportional Division

Sometimes we need to divide an amount up according to a particular ratio.
This is sometimes called "division in a given ratio".

## Example Question

Julie and Jack run a stall at a car boot sale, and take a total of £90.
They decide to share the money in the ratio 4:5. How much does each get?

The first step is to work out the total number of parts in the ratio.
Julie is getting 4 parts and Jack is getting 5 parts, so the total is 9 parts.

Next, we work out what 1 part is worth.
The total to be shared is £90, which is 9 parts, so 1 part will be £90÷9 = £10.

Finally, we work out what each person's share is worth.
Julie's share is 4 parts, so she will get 4×£10 = £40.
Jack's share is 5 parts, so he will get 5×£10 = £50.

A good check is to make sure that the answers add up to the original total. In this case £40 + £50 = £90.

Practice Question
Work out the answer to each part of this question then click to see whether you are correct.

Rachel, Ben and Emma are given 52 sweets.
They decide to share their sweets in the ratio of their ages, 10 : 9 : 7.

What is the total number of parts in the ratio? How many sweets is one of the parts worth? How many sweets does Rachel get? How many sweets does Ben get? How many sweets does Emma get? ## Exercises

Work out the answers to the questions below and fill in the boxes. Click on the button to find out whether you have answered correctly. If you are right then will appear and you should move on to the next question. If appears then your answer is wrong. Click on to clear your original answer and have another go. If you can't work out the right answer then click on to see the answer.

Question 1
 (a) Divide £50 in the ratio 2:3     £ and £  (b) Divide £100 in the ratio 1:4     £ and £  (c) Divide £60 in the ratio 11:4     £ and £  (d) Divide 80kg in the ratio 1:3     kg and kg  Question 2
 (a) Divide £60 in the ratio 6:5:1     £ and £ and £  (b) Divide £108 in the ratio 3:4:5     £ and £ and £  (c) Divide 30kg in the ratio 1:2:3     kg and kg and kg  (d) Divide 75 litres in the ratio 12:8:5     litres and litres and litres  Question 3
Heidi and Briony get £80 by selling their old toys at a car boot sale.
They divide the money in the ratio 2:3.

How much money do they each receive?
Heidi gets £
Briony gets £  Question 4
In a chemistry lab, acid and water are mixed in the ratio 1:5.
A bottle contains 216ml of the mixture.

How much acid and how much water were needed to make this amount of the mixture?
ml of acid
ml of water  Question 5
Blue and yellow paints are mixed in the ratio 3:5 to produce green paint.

How much of each colour are needed to produce 40ml of green paint?
ml of blue paint
ml of yellow paint  Question 6
Simon, Sarah and Matthew are given a total of £300.
They share it in the ratio 10:11:9.

Simon gets £
Sarah gets £
Matthew gets £  Question 7
In a fruit cocktail drink, pineapple juice, orange juice, and apple juice are mixed in the ratio 7:5:4.
 (a) How much of each juice do you need to make 80ml of the cocktail? ml of pineapple juice ml of orange juice ml of apple juice  (b) How much of each juice do you need to make 800ml of the cocktail? ml of pineapple juice ml of orange juice ml of apple juice  Question 8
Blue, red and yellow paints are mixed to produce 200ml of another colour.

How much of each colour are required if they are mixed in the ratio:
 (a) 1:1:2 ml of blue paint ml of red paint ml of yellow paint  (b) 3:3:2 ml of blue paint ml of red paint ml of yellow paint  (c) 9:4:7 ml of blue paint ml of red paint ml of yellow paint  Question 9
To start up a small business, it is necessary to spend £800.
Paul, Margaret and Denise agree to contribute in the ratio 8:1:7.

How much does each need to spend?
Paul: £
Margaret: £
Denise: £  You have now completed Unit 7 Section 3
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