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Dividing into a Ratio (One Part or Difference)

In this worksheet. Students practise how to deal with ratios where only one part is given or the difference between the ratios is given.

'Dividing into a Ratio (One Part or Difference)' worksheet

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:  

Worksheet Overview

QUESTION 1 of 10

This lesson covers the two elements of ratio that frequently catch students out.

As with all other ratio questions though, the trick is finding what one part is worth.

 

Example 1: One part of the ratio is given.

Orange Juice is made from concentrate and water in the ratio 2:5.

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

Step 1: Identify how many parts the number you are told is worth.

We are told that we use 300 ml of concentrate. In the ratio, we are told that this is worth 2 parts

Step 2: Find out what 1 part is worth

We know that 2 parts is 300 ml

So one part must be 150 ml

Step 3: Work out the answer

We are asked for how much water we need and we are told that this is 5 parts.

5 x 150 ml = 750 ml

 

Example 2: The difference is given

Two people split some money into the ratio 2:7.

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

Step 1: Identify how many parts the number you are told is worth.

We are told that we use £250 is the difference between the 7 parts and the 2 parts. This means it must be worth 5 parts.

Step 2: Find out what 1 part is worth

We know that 5 parts is £250

So one part must be $50

Step 3: Work out the answer

We are asked for how much was split in total. This is both the 2 and 7 parts so 9 parts in total

9 x £50 = £450

All ratio questions should be approached by trying to find out the value of how many parts?

I buy plain crisps and beef flavored crisps in the ratio of 5:3.

If I buy 60 bags of beef crisps, how many bags do I buy in total?

I buy 100 chocolate bars. Which of the following ratios could I split the bars into without breaking the bars into pieces?

1:9

2:10

3:2

16:9

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

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

1:9

2:10

3:2

16:9

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

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

 

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

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

 

I am trying to answer the question...

 

A length of wood is split into the ratio of 1:4

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

 

On which line of the following working do I make the first 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 x 14 = 14 cm

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

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

Line 1

Line 2

Line 3

Line 4

Line 5

Line 6

Match the ratio and the difference to the total amount.

Column A

Column B

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

One side of 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?

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

 

Which of the following numbers would be the most sensible to choose?

10

20

40

70

  • Question 1

All ratio questions should be approached by trying to find out the value of how many parts?

CORRECT ANSWER
1
One
one
EDDIE SAYS
ALL ratio questions have the same core process. Trying to find out what one part is worth and then using that to find the answer.
  • Question 2

I buy plain crisps and beef flavored crisps in the ratio of 5:3.

If I buy 60 bags of beef crisps, how many bags do I buy in total?

CORRECT ANSWER
160
EDDIE SAYS
We are told that 60 bags of beef crisps represents 3 parts. Next we need to find out how many bags 1 part is worth (20) How do we use this to find the TOTAL?
  • Question 3

I buy 100 chocolate bars. Which of the following ratios could I split the bars into without breaking the bars into pieces?

CORRECT ANSWER
1:9
3:2
16:9
EDDIE SAYS
If I want to split the bars without breaking into them. The total in the ratio must add up to a factor of 5 For example 3:2 makes 5 parts. I can split 100 into 5 parts.
  • Question 4

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

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

CORRECT ANSWER
EDDIE SAYS
We know that James gets £600 and his share is worth 3 parts. This means that 1 part must be worth £200
  • Question 5

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

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

 

CORRECT ANSWER
200
EDDIE SAYS
180 second class seats is 9 parts. Find one part (20 seats) In total we have 10 parts.
  • Question 6

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

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

 

CORRECT ANSWER
EDDIE SAYS
This is a difference question. We can see that the difference (£750) is 3 parts. This gives 1 part as £250 We can now use this to find the lower earner (2 parts)
  • Question 7

I am trying to answer the question...

 

A length of wood is split into the ratio of 1:4

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

 

On which line of the following working do I make the first 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 x 14 = 14 cm

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

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

CORRECT ANSWER
Line 3
EDDIE SAYS
The mistake is on line 3. If 3 parts is worth 45 cm. I need to divide by 3 to get 1 part which should give me 15cm (The rest of the working afterwards is ok as I have correctly used this mistake)
  • Question 8

Match the ratio and the difference to the total amount.

CORRECT ANSWER

Column A

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 1) Find one part 2) Use this to find the total For example 2:5 has a difference of 3 parts. If this is worth 30, one part is 10. 2:5 has 7 parts in total so the total is worth 70
  • Question 9

One side of 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?

CORRECT ANSWER
160
160 m
160m
EDDIE SAYS
The two longest sections are the 2 parts and the 5 parts. The difference between these is 3 parts and is worth 60 m. This means that 1 part is worth 20 m How many parts are there in total?
  • Question 10

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

 

Which of the following numbers would be the most sensible to choose?

CORRECT ANSWER
40
EDDIE SAYS
Never try to make your life difficult The ratio 1: 2 : 5 adds up to 8 so we need a number that can easily be divided by 8. Without dealing with decimals, the only numbers in the 10 times tables that you can do this are 40 and 80
---- OR ----

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