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 909 = 10.

Finally, we work out what each person's share is worth.
Julie's share is 4 parts, so she will get 4ף10 = 40.
Jack's share is 5 parts, so he will get 5ף10 = 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 Click on this button below to see the correct answer 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 Click this button to see if you are correct 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 Click on this button to see the correct answer 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.

How much does each receive?
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:


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Produced by A.J.Reynolds October 2003
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