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

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(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

(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

(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

(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