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Write a Ratio from Amounts

In this worksheet, students will practise creating ratios to compare two quantities which have something in common. They will express these ratios in the form a:b, but will not be asked to simplify at this point.

'Write a Ratio from Amounts' 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

What Is a Ratio?

A ratio is simply a way of comparing two or more quantities.

 

 

What Does a Ratio Look Like?

A ratio is just two numbers written with a colon between them,

e.g. 3:5  2:7 etc.

 

 

Does the Order Matter?

Yes, absolutely it does!

3:1 is not the same as 1:3, so always take care with the order.

 

 

Let's look at ratio in action in an example now.

 

 

 

e.g. I have 4 red balls and 6 blue balls. Write a ratio for the amount of red balls to blue balls.

 

Look carefully at the question here - we are asked to find 'red balls to blue balls'.

So the ratio we need to use will be expressed as:

Red:Blue

 

Now we just need to substitute the correct numbers into this ratio:

4:6

 

While this ratio can be cancelled down, don't worry about that at this point, we will focus on learning how to do this in the Level 2 activity on ratio. 

 

 

 

In this activity, we will create ratios to compare two quantities which have something in common. We will express these ratios in the form a:b, but we will not be simplifying them at this point. 

In a bag, there are 3 red balls and 6 blue balls.

 

Write a ratio to express the number of red balls in relation to the number of blue balls.

In a bag, there are 4 red balls and 5 blue balls.

 

Which of the ratios below could be correct expressions of this relationship? 

4:5

5:4

Both

In a class, there are twice as many boys as girls.

 

What is the ratio of boys to girls in the class?

4:5

5:4

Both

In the same class, there are twice as many boys as girls.

 

What is the ratio of girls to boys in the class?

4:5

5:4

Both

A girls has 7 dark chocolates and 10 milk ones left in a box.

 

Which of the options below is the correct ratio to compare dark and milk chocolates?

7:10

10:7

Both are correct

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

7:10

10:7

Both are correct

Match each scenario on the left with the correct ratio on the right. 

Column A

Column B

10 boys and 15 girls; Boys:Girls
5:3
10 boys and 15 girls; Girls to boys
15:10
3 red balls and 5 green balls; Green to red
10:15
3 veg pies and 5 meat pies; Veg to meat
3:5

A car drives at a rate of 42 miles per gallon (mpg) of petrol, while a motorbike drives at a rate of 63 mpg.

 

Write a ratio to compare the mpg for the motorbike to the car.

Column A

Column B

10 boys and 15 girls; Boys:Girls
5:3
10 boys and 15 girls; Girls to boys
15:10
3 red balls and 5 green balls; Green to red
10:15
3 veg pies and 5 meat pies; Veg to meat
3:5

A boy has 6 oranges and 9 apples.

 

Write a ratio to compare the number of oranges he has to apples. 

Column A

Column B

10 boys and 15 girls; Boys:Girls
5:3
10 boys and 15 girls; Girls to boys
15:10
3 red balls and 5 green balls; Green to red
10:15
3 veg pies and 5 meat pies; Veg to meat
3:5

The width of a rectangle is three times as long as its height. 

 

Write a ratio to compare the width of the rectangle to its height.

Column A

Column B

10 boys and 15 girls; Boys:Girls
5:3
10 boys and 15 girls; Girls to boys
15:10
3 red balls and 5 green balls; Green to red
10:15
3 veg pies and 5 meat pies; Veg to meat
3:5
  • Question 1

In a bag, there are 3 red balls and 6 blue balls.

 

Write a ratio to express the number of red balls in relation to the number of blue balls.

CORRECT ANSWER
EDDIE SAYS
Here we are asked for the 'number of red balls in relation to the number of blue balls', which we will express as: Red:Blue Now let's put the correct numbers in to represent these amounts: 3:6 Make sure you get these amounts the correct way round or your answer will not be correct.
  • Question 2

In a bag, there are 4 red balls and 5 blue balls.

 

Which of the ratios below could be correct expressions of this relationship? 

CORRECT ANSWER
Both
EDDIE SAYS
This was a bit of a trick question! The order of a ratio is incredibly important, and if definitely needs to match what is requested. However, the question here doesn't specify the order of the ratio, so both options are valid answers in this case.
  • Question 3

In a class, there are twice as many boys as girls.

 

What is the ratio of boys to girls in the class?

CORRECT ANSWER
EDDIE SAYS
This ones needs a little detective work, as there are no numbers present. We are told that there are 'twice as many boys' in the class than girls. This means there are 2 boys to every 1 girl. We are asked for the ratio of boy:girls. If we substitute the correct numbers into this ratio, we reach 2:1.
  • Question 4

In the same class, there are twice as many boys as girls.

 

What is the ratio of girls to boys in the class?

CORRECT ANSWER
EDDIE SAYS
We are working with the same class here, but we are being asked to find a different ratio. We are asked for the ratio of girls:boys this time. If we substitute the correct numbers into this ratio, we reach 1:2. Can you see that this uses the same numbers as the previous ratio, but their order has been flipped?
  • Question 5

A girls has 7 dark chocolates and 10 milk ones left in a box.

 

Which of the options below is the correct ratio to compare dark and milk chocolates?

CORRECT ANSWER
7:10
EDDIE SAYS
This time, the question does specify an order for our ratio. It asks for 'the correct ratio to compare dark and milk chocolates', so we are looking for dark:milk. Now let's substitute the correct numbers into this worded ratio: 7:10 This time, it is not acceptable to express this ratio the other way round as this is not the correct answer to match what is requested in the question.
  • Question 6

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

CORRECT ANSWER
EDDIE SAYS
Can you recall the purpose of a ratio, which was explained in the Introduction? Ratios are used to compare quantities which have something in common.
  • Question 7

Match each scenario on the left with the correct ratio on the right. 

CORRECT ANSWER

Column A

Column B

10 boys and 15 girls; Boys:Girls
10:15
10 boys and 15 girls; Girls to bo...
15:10
3 red balls and 5 green balls; Gr...
5:3
3 veg pies and 5 meat pies; Veg t...
3:5
EDDIE SAYS
The most important thing here is to match the correct numbers in each ratio, plus to match the correct order. Let's work through each scenario one at a time. 1) Boys:Girls --> 10:15 2) Girls:Boys --> 15:10 3) Green:Red --> 5:3 4) Veg:Meat --> 3:5 Were you able to match those scenarios and ratios successfully?
  • Question 8

A car drives at a rate of 42 miles per gallon (mpg) of petrol, while a motorbike drives at a rate of 63 mpg.

 

Write a ratio to compare the mpg for the motorbike to the car.

CORRECT ANSWER
EDDIE SAYS
Did you spot that we are asked for the ratio of motorbike:car? Now let's substitute the correct numbers into this worded ratio: 63:42 Again, the order here is very important, so 42:63 is not an acceptable answer.
  • Question 9

A boy has 6 oranges and 9 apples.

 

Write a ratio to compare the number of oranges he has to apples. 

CORRECT ANSWER
EDDIE SAYS
Here we are asked for the ratio of oranges:apples. Now let's substitute the correct numbers into this worded ratio: 6:9 Again, the order here is very important, so 9:6 is not an acceptable answer.
  • Question 10

The width of a rectangle is three times as long as its height. 

 

Write a ratio to compare the width of the rectangle to its height.

CORRECT ANSWER
EDDIE SAYS
This ones needs a little detective work, as there are no numbers present. We are told that 'the width...is three times as long as its height'. This means there are three units in the width to every one in the height. We are asked for the ratio of width:height. If we substitute the correct numbers into this ratio, we reach 3:1. Well done for completing this activity - you can now create ratios to compare two quantities which have something in common. If you are feeling confident, why not try the Level 2 activity on this theme?
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