# Understand Dividing into a Given Ratio

In this worksheet, students will split amounts into given ratios using the method of finding the total number of parts, dividing by this value, and then multiplying by each value in the 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

In exams, it is common to encounter problems where you are asked to split (or share) an amount into a given ratio.

We will be focusing on this skill during this activity.

The key to solving this type of question, as with all ratio questions, is to consider what 1 part is worth.

Let's look at an example to follow this process through.

e.g. Split £100 into the ratio 2:3.

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

With the ratio 2:3, there are 5 parts in total (as 2 + 3 = 5).

So if we are splitting £100 into 5 equal parts, each one is worth £20 (as £100 ÷ 5).

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

The 2 in the ratio represents two (of the total five) parts, so this is worth: 2 × £20 = £40

The 3 in the ratio represents three (of the total five) parts, so this is worth: 3 × £20 = £60

The final step is to check we have the correct answers by adding them together.

Do they add up to the £100 we started with?

Yes, so we can be 100% sure that our answers are correct.

In this activity, we will split amounts into given ratios using the method demonstrated above of finding the total number of parts, dividing by this value, and then multiplying by each value in the ratio.

Type a word into the space to complete the sentence below.

If we split £200 into 5 parts, how much is each part worth?

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

Split £180 into the ratio 1:3.

Type your answer as a number only without units, as these have already been provided for you.

Split £320 into the ratio 3:5.

Type your answer as a number only without units, as these have already been provided for you.

On the left are four amounts with the ratios they need to be split into.

Match each amount and ratio with its correct pair of values.

## Column B

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

James and John wash cars together and earn £100

They share the earnings in the ratio 2:3.

How much does John get?

Type your answer as a number only without units, as these have already been provided for you.

## Column B

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

David is 14 and his brother Simon is 16.

They split a £300 inheritance in the ratio of their ages.

How much do they each receive?

Type your answer as a number only without units, as these have already been provided for you.

## Column B

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

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

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

David gets 12 cm of chocolate, whilst John gets 8 cm.

Have they shared the chocolate correctly in the ratio they had planned?

Yes

No

• Question 1

Type a word into the space to complete the sentence below.

EDDIE SAYS
Did you recall this key part of the process from the Introduction? In order to split an amount into a number of parts, we must first find the total number of parts by adding the two numbers in our starting ratio together. Remember this important step to help you in the rest of this activity. Review the Introduction now to refresh on the whole process, if you need to, before you move on.
• Question 2

If we split £200 into 5 parts, how much is each part worth?

EDDIE SAYS
To find the value of each part, we simply divide the total amount by the number of parts: 200 ÷ 5 = 40 So each of the 5 parts represents £40 in this case.
• Question 3

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

EDDIE SAYS
To find the value of each part, we simply divide the total amount by the number of parts. This time, it is easier to express '2 hours' in minutes before we start, as we are asked to express our answer in minutes. There are 60 minutes in 1 hour, so 2 h = 120 m. 120 ÷ 6 = 20 So each of the 6 parts represents 20 minutes.
• Question 4

Split £180 into the ratio 1:3.

Type your answer as a number only without units, as these have already been provided for you.

EDDIE SAYS
Our first step here is to consider how many total parts we need to split our amount into. With the ratio 1:3, there are 4 parts in total (as 1 + 3 = 4). So if we are splitting £180 into 4 equal parts, each one is worth £45 (as 180 ÷ 4 = 45). Now we need to calculate what each section of the ratio is worth. The 3 in the ratio represents three (of the total four) parts, so this is worth: 3 × £45 = £135 The 1 in the ratio represents one (of the total four) parts, so this is worth: 1 × £45 = £45 Do they add up to the £180 we started with? £135 + £45 = £180, so we can be totally sure that we have the correct answers.
• Question 5

Split £320 into the ratio 3:5.

Type your answer as a number only without units, as these have already been provided for you.

EDDIE SAYS
With the ratio 3:5, there are 8 parts in total (as 3 + 5 = 8). So if we are splitting £320 into 8 equal parts, each one is worth £40 (as 320 ÷ 8 = 40). Now we need to calculate what each section of the ratio is worth: 3 × £40 = £120 5 × £40 = £200 Let's check our answer: £120 + £200 = £320, which was our starting value!
• Question 6

On the left are four amounts with the ratios they need to be split into.

Match each amount and ratio with its correct pair of values.

## 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 our rules: 1) Add the ratio together; 2) Divide by this; 3) Multiply each part of the ratio by this value. Let's look at the first pair as an example together. 210 into the ratio 3:4 3 + 4 = 7 210 ÷ 7 = 30 30 × 3 = 90; 30 × 4 = 120 Can you use this example to successfully identify the other matches?
• Question 7

James and John wash cars together and earn £100

They share the earnings in the ratio 2:3.

How much does John get?

Type your answer as a number only without units, as these have already been provided for you.

EDDIE SAYS
This one is a little different, as we need to link the ratios to a person too. Let's follow our rules first. 1) Add the ratio together > 2 + 3 = 5 2) Divide by this > 100 ÷ 5 = £20 3) Multiply each part of the ratio by this value > 2 × 20 = £40 3 × 20 = £60 But which of these amounts should be John's? In our question, John was the second person mentioned, so he gets the second amount, which is £60.
• Question 8

David is 14 and his brother Simon is 16.

They split a £300 inheritance in the ratio of their ages.

How much do they each receive?

Type your answer as a number only without units, as these have already been provided for you.

EDDIE SAYS
The challenge here is in finding the ratio to use. We are told that the inheritance needs to be split 'in the ratio of their ages'. This means 14:16. Once we have this, we can calculate as normal. 1) Add the ratio together > 14 + 16 = 30 2) Divide by this > 300 ÷ 30 = £10 3) Multiply each part of the ratio by this value > 14 × 10 = £140 16 × 10 = £160 Be sure to link the correct ratio (which represents an age), with the correct brother's name.
• 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 is a little confusing. Firstly, we need to convert our starting amount into minutes to be able to split it easily. There are 60 minutes in 1 hour, so 3 h = 180 m. Now let's follow our regular rules. 1) Add the ratio together > 5 + 7 = 12 2) Divide by this > 180 ÷ 12 = 15 mins 3) Multiply each part of the ratio by this value > 5 × 15 = 75 mins 7 × 15 = 105 mins We then need to convert these values back into hours and minutes to express our answer in the requested format.
• Question 10

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

David gets 12 cm of chocolate, whilst John gets 8 cm.

Have they shared the chocolate correctly in the ratio they had planned?

No
EDDIE SAYS
Let's follow our rules for the final time in this activity. 1) Add the ratio together > 2 + 3 = 5 2) Divide by this > 20 ÷ 5 = 4 cm 3) Multiply each part of the ratio by this value > 2 × 4 = 8 cm 3 × 4 = 12 cm So the amounts are correct, but have the ratios been correctly linked with the right boy? The questions says that David received '12 cm of chocolate', but as he was represented by the second ratio, he should only have received 8 cm. So the amounts and the ratios have got mixed up! Take care to avoid a similar error in your own working. Congratulations! You can now split amounts into given ratios using the method of finding the total number of parts, dividing by this value, and then multiplying by each value in the ratio.
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