# Divide into a Ratio (when given One Part or Difference)

In this worksheet, students will divide amounts into ratios when one part of the ratio or the difference between the amounts has been provided, by finding the value of one part and applying this knowledge to solve a problem.

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

This activity focuses on the two elements of ratio that frequently catch students out - finding a missing amount when provided with one part of the ratio to use or the difference between the two amounts

As with all ratio questions, the key to success is finding what one part is worth.

Let's look at these concepts in action in a pair of examples.

One Part of the Ratio Given

e.g. Orange squash is made from concentrate and water in the ratio 2:5.

If we use 300 ml of concentrate, how much water do we need to use?

Step 1: Identify how many parts the amount you have is worth.

We are told that we use 300 ml of concentrate.

In the ratio, we are told that this is worth 2 parts of the total amount.

Step 2: Find out what one part is worth.

We know that 2 parts represents 300 ml in total.

So 1 part must represent 150 ml.

Step 3: Use the information gathered to work out the answer.

We are asked '...how much water do we need to use?'

We are also told that the water element represents 5 parts in the ratio.

5 × 150 ml = 750 ml

So we will need to use 750 ml of water with 300 ml of concentrate to create orange squash in the ratio requested.

The Difference is Given

e.g. Two people split some money in the ratio 2:7.

If one gets £250 more than the other, how much money do they split in total?

Step 1: Identify how many parts the amount you have is worth.

We are told that £250 is the difference between the 7 parts and the 2 parts.

This means that it must be worth 5 parts.

Step 2: Find out what one part is worth.

We know that 5 parts represents £250.

So 1 part must represent £50.

Step 3: Use the information gathered to work out the answer.

We are asked '...how much money do they split in total?'

This means we need to find the value of all the parts, so 9 parts in total (as 2 + 7 = 9).

9 × 50 = £450

So the two people in the question originally split £450 in the ratio 2:7.

In this activity, we will divide amounts into ratios, when one part of the ratio to use or the difference between the amounts has been provided, using the method shown above.

All ratio questions should be approached by first finding the value of how many parts?

Josie buys plain and beef flavored crisps in the ratio of 5:3.

If she buys 60 bags of beef crisps, how many bags of crisps does she buy in total?

Which of the ratios below could he split the bars into without breaking the bars into pieces?

1:9

2:10

3:2

16:9

James and Husna split their business profits into the ratio of 3:7.

If James gets £600, how much does Husna get?

1:9

2:10

3:2

16:9

The ratio of first class to second class seats on a train is 1:9.

If there are 180 second class seats, how many seats are on the train in total?

1:9

2:10

3:2

16:9

Two business partners split their monthly income in the ratio 2:5.

If one gets £750 more than the other, how much does the other earner receive?

1:9

2:10

3:2

16:9

A length of wood is cut in half in the ratio of 1:4.

If one piece is 45 cm longer than the other, how long was the original piece of wood?

They have written the working below, but have made ONE mistake.

Line 1: Difference in lengths = 4 - 1 = 3 parts

Line 2: 3 parts = 45 cm

Line 3: 1 part = 14 cm

Line 4: The first part is 1 × 14 = 14 cm

Line 5: The second part is 4 × 14 = 56 cm

Line 6: The wood was originally 14 + 56 = 70 cm long

On which line does their error occur?

Line 1

Line 2

Line 3

Line 4

Line 5

Line 6

On the left are four ratios with the difference between two amounts provided.

Match each ratio and difference with its correct starting total.

## Column B

2:5, Difference = 30
70
3:7, Difference = 8
45
1:10, Difference = 27
40
5:1, Difference = 30
33

A football field is split into the ratio 1:2:5.

If the difference in lengths between the two largest sections is 60 m, how long is the field in total?

## Column B

2:5, Difference = 30
70
3:7, Difference = 8
45
1:10, Difference = 27
40
5:1, Difference = 30
33

A teacher asks a pupil to choose a number in the 10 times table and then to split this in the ratio 1:2:5.

Which of the numbers below would be the most sensible option to choose?

10

20

40

70

• Question 1

All ratio questions should be approached by first finding the value of how many parts?

One
1
EDDIE SAYS
All ratio questions have the same core process at their heart. We always need to start by finding the value which one part is worth, and then applying this knowledge to find the answer to the problem. Remember this essential first step to support you in the remainder of this activity.
• Question 2

Josie buys plain and beef flavored crisps in the ratio of 5:3.

If she buys 60 bags of beef crisps, how many bags of crisps does she buy in total?

EDDIE SAYS
Let's apply our process from the Introduction. Step 1: Identify how many parts the amount you have is worth. We are told that we have 60 bags of beef crisps. In the ratio, we are told that this is worth 3 parts of the total amount. Step 2: Find out what one part is worth. We know that 3 parts represents 60 bags in total. So 1 part must represent: 60 ÷ 3 = 20 bags. Step 3: Use the information gathered to work out the answer. We are asked for the total number of bags, which we know is represented by 8 parts in the ratio. 8 × 20 = 160 bags
• Question 3

Which of the ratios below could he split the bars into without breaking the bars into pieces?

1:9
3:2
16:9
EDDIE SAYS
If Sam wants to split the bars without breaking them, then the total number of parts in the ratio must add up to a factor of 5. For example, the ratio 3:2 has 5 parts in total. We can split 100 into 5 parts evenly, with no remainders, so this option is a viable ratio to use. Can you find the other two viable ratios independently which can be used in this case?
• Question 4

James and Husna split their business profits into the ratio of 3:7.

If James gets £600, how much does Husna get?

EDDIE SAYS
Remember the steps to follow: 1) Identify how many parts; 2) Find the value of one part; 3) Use this info to find the starting total. 1) James gets £600 and his share represents 3 parts. 2) So one part is represented by £200 (600 ÷ 3). 3) Husna's income represents 7 parts so can be found by calculating: 7 × 200 = £1,400
• Question 5

The ratio of first class to second class seats on a train is 1:9.

If there are 180 second class seats, how many seats are on the train in total?

EDDIE SAYS
Let's apply our process again. Step 1: We are told that we have 180 seats in second class. In the ratio, we are told that this is worth 9 parts of the total amount. Step 2: We know that 9 parts represents 180 seats. So 1 part must represent: 180 ÷ 9 = 20 seats. Step 3: We are asked for the total number of seats, which we know is represented by 10 parts in the ratio. 10 × 20 = 200 seats
• Question 6

Two business partners split their monthly income in the ratio 2:5.

If one gets £750 more than the other, how much does the other earner receive?

EDDIE SAYS
This is a difference question. We can see that the difference of £750 represents 3 parts. So 1 part represents £250. The lower earner in the partnership represents 2 parts of the total, so we can find this amount by calculating: 2 × 250 = £500
• Question 7

A length of wood is cut in half in the ratio of 1:4.

If one piece is 45 cm longer than the other, how long was the original piece of wood?

They have written the working below, but have made ONE mistake.

Line 1: Difference in lengths = 4 - 1 = 3 parts

Line 2: 3 parts = 45 cm

Line 3: 1 part = 14 cm

Line 4: The first part is 1 × 14 = 14 cm

Line 5: The second part is 4 × 14 = 56 cm

Line 6: The wood was originally 14 + 56 = 70 cm long

On which line does their error occur?

Line 3
EDDIE SAYS
The mistake has been made on line 3. If 3 parts are worth 45 cm (line 2), then your friend needs to divide by 3 to find what 1 part is worth. 45 ÷ 3 = 15 cm but they have reached an answer of 14 cm instead. This means that after Line 3 the rest of their working, although correct in method, is wrong, as they have used the incorrect value for one part. It is important to record your working accurately in an exam, because your friend would still earn some marks for their method in this case, even though they reached an incorrect answer.
• Question 8

On the left are four ratios with the difference between two amounts provided.

Match each ratio and difference with its correct starting total.

## Column B

2:5, Difference = 30
70
3:7, Difference = 8
40
1:10, Difference = 27
33
5:1, Difference = 30
45
EDDIE SAYS
Remember the steps to follow: 1) Identify how many parts; 2) Find the value of one part; 3) Use this info to find the starting total. Let's work through the first pair as an example. 2:5, Difference = 30 1) 3 parts represent the difference of 30 2) 1 part represents 10 (30 ÷ 3) 3) 7 parts (2 + 5) represents the total, so 7 × 10 = 70 Can you use this example to calculate the other starting totals and find the matches independently?
• Question 9

A football field is split into the ratio 1:2:5.

If the difference in lengths between the two largest sections is 60 m, how long is the field in total?

EDDIE SAYS
The two largest sections of the field represent 2 parts and 5 parts. The difference between these is 3 parts and is worth 60 m. So 1 part is worth 20 m. The total is represented by 8 parts (1 + 2 + 5), so we can find this by calculating: 8 × 20 = 160 m
• Question 10

A teacher asks a pupil to choose a number in the 10 times table and then to split this in the ratio 1:2:5.

Which of the numbers below would be the most sensible option to choose?

40
EDDIE SAYS
The ratio 1:2:5 adds up to 8 parts in total, so we need to find a number that can easily be divided by 8. Let's not make our life harder than it needs to be! Without dealing with decimals, the only numbers in the 10 times table which also appear in the 8 times table, are 40 and 80. So, out of the options provided, 40 is the most sensible number to choose to work with. You can now divide amounts into ratios when one part of the ratio or the difference between the amounts has been provided, by finding the value of one part and applying this knowledge to solve a problem - great work!
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