 # Understand Dividing into a Given Ratio

In this worksheet, students practise dividing an amount into a given ratio. Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   AQA, Eduqas, Pearson Edexcel, OCR

Curriculum topic:   Ratio, Proportion and Rates of Change

Curriculum subtopic:   Ratio, Proportion and Rates of Change, Calculations with Ratio

Difficulty level:   ### QUESTION 1 of 10

There is a very common problem in Maths where you are asked to split (or share) an amount into a given ratio,

The keyto solving these questions, as with all ratio questions, is to consider what 1 part is worth.

Example 1: Split £100 into the ratio 2:3?

Our first step here is to consider how many parts we need to split into.

With the ratio 2:3, there are 5 parts in total.

So if we are splitting £100 into 5 equal parts, each one is worth £20  (£100 &div; 5)

Now we need to find what each section of the ratio is worth.

The 2 in the ratio is two parts, so this is worth 2 x £20 = £40

The 3 in the ratio is three parts, so this is worth 3 x £20 = £60

The last step is to check we have got this correct by adding them together. Do they add up to the £100 we started with?

The first step when splitting into a given ratio is to...

If I split £200 into 5 parts. How much is each part worth.

If I split 2 hours into 6 parts, how many minutes is each part worth?

Split £180 into the ratio 1:3

Split £320 into the ratio 3:5

Here are 4 amounts and the ratio they have been split into. Match these with the answers.

## Column B

210 into the ratio 3:4
20 and 80
350 into the ratio 2:5
200 and 150
100 into the ratio 1:4
90 and 120
350 into the ratio 4:3
100 and 250

James and John split £100 into the ratio 2:3.

How much does John get?

## Column B

210 into the ratio 3:4
20 and 80
350 into the ratio 2:5
200 and 150
100 into the ratio 1:4
90 and 120
350 into the ratio 4:3
100 and 250

David is 14 and his brother Simon is 16.

They split £300 in the ratio of their ages.

## Column B

210 into the ratio 3:4
20 and 80
350 into the ratio 2:5
200 and 150
100 into the ratio 1:4
90 and 120
350 into the ratio 4:3
100 and 250

If I split 3 hours into the ratio 5:7. How many hours and minutes would be in each part?

## Column B

210 into the ratio 3:4
20 and 80
350 into the ratio 2:5
200 and 150
100 into the ratio 1:4
90 and 120
350 into the ratio 4:3
100 and 250

Has this ratio been split correctly?

David and John split a 20cm chocolate bar into the ratio 2:3

David gets 12cm and John gets 8cm

Yes

No

• Question 1

The first step when splitting into a given ratio is to...

EDDIE SAYS
A nice and easy one, before you find out what one part is worth, you need to find the total number of parts. Another word for total is add
• Question 2

If I split £200 into 5 parts. How much is each part worth.

EDDIE SAYS
All five parts are worth the same so all we do is divide. £200 ÷ 5
• Question 3

If I split 2 hours into 6 parts, how many minutes is each part worth?

20
EDDIE SAYS
Just remember that with questions like this, you can always change the units if it makes life easier. 2 hours is 120 minutes If this is worth 6 parts, how much is one part worth?
• Question 4

Split £180 into the ratio 1:3

EDDIE SAYS
Splitting an amount into the ratio 1:3 means we are splitting it into 4 parts 4 parts is £180 This means 1 part is worth £45 How can you use this to get the final answers?
• Question 5

Split £320 into the ratio 3:5

EDDIE SAYS
Splitting an amount into the ratio 3:5 means we are splitting it into 8 parts 8 parts is £320 This means 1 part is worth £40 How can you use this to get the final answers?
• Question 6

Here are 4 amounts and the ratio they have been split into. Match these with the answers.

## Column B

210 into the ratio 3:4
90 and 120
350 into the ratio 2:5
100 and 250
100 into the ratio 1:4
20 and 80
350 into the ratio 4:3
200 and 150
EDDIE SAYS
Remember the rules. 1) Add the ratio together 2) Divide by this 3) MUltiply each part of the ratio by this answer
• Question 7

James and John split £100 into the ratio 2:3.

How much does John get?

EDDIE SAYS
This is a little bit different, we still approach it the same to find out the amounts (£40 and £60). We have to consider which one is John. Always remember that it will be the same order as the question. In our question John was the second person mentioned, so he gets the second amount.
• Question 8

David is 14 and his brother Simon is 16.

They split £300 in the ratio of their ages.

EDDIE SAYS
The hard part here is finding the ratio. You are told they split into the ratio of their ages, This would be 14:16 Once we have that, it's just the same as before.
• Question 9

If I split 3 hours into the ratio 5:7. How many hours and minutes would be in each part?

EDDIE SAYS
This can be confusing. Firstly we need to convert it into minutes to be able to split it. If we split it, we should get 75 minutes and 105 minutes. We then need to convert this back into hours and minutes.
• Question 10

Has this ratio been split correctly?

David and John split a 20cm chocolate bar into the ratio 2:3

David gets 12cm and John gets 8cm

No
EDDIE SAYS
Are the final answers the correct way round?
---- OR ----

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