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Understand One Amount as a Fraction of Another

In this worksheet, students will practise expressing amounts as fractions of each other and cancelling these fractions into their simplest forms, with and without units of measurements..

'Understand One Amount as a Fraction of Another' worksheet

Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   AQA, Eduqas, Pearson Edexcel, OCR

Curriculum topic:   Ratio, Proportion and Rates of Change, Fractions, Decimals and Percentages

Curriculum subtopic:   Ratio, Proportion and Rates of Change, Fractions

Difficulty level:  

Worksheet Overview

QUESTION 1 of 10

There are a number of times when we need to be able to write one number as a fraction of another, such as finding percentages, making recipes, distributing something between a group of people, etc. 

 

In this activity, you will learn how to do this quickly and easy, so that you have this skill ready to use in your exams and in your life. 

 

 

Let's review some examples to see how we calculate one number as a fraction of another. 

 

 

e.g. Write 25 as a fraction of 35.

 

The first step here is to write the number as a fraction.

'25 out of 35' should be expressed like this:  

25
35

 

Job done you think?

Not quite, we have to cancel fractions into their simplest possible forms. 

 

To do this, we need to look for the Highest Common Factor (HCF).

To remind you, the HCF is the largest number which you can divide both the values in your fraction by.

 

In this case, it's 5:

 

25
35
=
25 ÷ 5
35 ÷ 5
=
5
7

 

 

 

e.g. Write 10 m as a fraction of 30 m.

 

In this example, we have been given units ('metres').

That's not a problem here as the units used are the same with both numbers so they will cancel in the fraction in the same way:

 

10
30
=
10 ÷ 10
30 ÷ 10
=
1
3

 

 

 

e.g. Write 25 p as a fraction of £3.

 

This example is a little more complicated.

As the units used in the question are not the same, we have to make them the same before we start. 

There is 100 p in £1, so £3 = 300 p.

 

Now the units are the same, we can just proceed as we did in the other examples: 

 

25
300
=
25 ÷ 25
300 ÷ 25
=
1
12

 

 

 

In this activity, we will practise expressing amounts as fractions of each other and cancelling these fractions into their simplest forms, with and without units of measurements.

Write the following fraction in its simplest form:

 

30
75

 

Type your answer in the form a/b without any spaces and using the / key to create your fraction bar. 

Which of the following fractions represents 12 out of 18?

12/18

2/3

4/6

6/9

1/4

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

12/18

2/3

4/6

6/9

1/4

Match each pair of amounts on the left with the correct fraction to compare them on the right. 

Column A

Column B

15 as a fraction of 25
4/10
20 as a fraction of 30
15/25
40p as a fraction of 80p
20/30
4m as a fraction of 10m
40/80

Match each verbal comparison on the left with the correct simplified fraction on the right. 

Column A

Column B

15 as a fraction of 25
2/3
20 as a fraction of 30
1/2
40p as a fraction of 80p
2/5
4m as a fraction of 10m
3/5

What is 10 out of 20 as a fraction in its simplest form?

 

Type your answer in the form a/b without any spaces and using the / key to create your fraction bar. 

What is 32 kg as a fraction of 80 kg?

 

Type your answer in the form a/b without any spaces and using the / key to create your fraction bar.

What is 30 p as a fraction of £2 in its simplest possible form?

 

Type your answer in the form a/b without any spaces and using the / key to create your fraction bar.

For each question shown, state if the fraction given as an answer is right and in its simplest form

 

Mark each question and answer as either 'Correct' or 'Incorrect' by selecting one option for each in the table. 

5 minutes as a fraction of 1 hr is 1/20.

 

Is this statement correct?

Yes

No

  • Question 1

Write the following fraction in its simplest form:

 

30
75

 

Type your answer in the form a/b without any spaces and using the / key to create your fraction bar. 

CORRECT ANSWER
2/5
EDDIE SAYS
To cancel this fraction into its simplest form, we have to divide both numbers by the Highest Common Factor (HCF). Let's ask ourselves: "What is the largest number which we can divide both 30 and 75 by?" The largest number we can divide both numbers by is 15:
30 ÷ 15  = 2
75 ÷ 15 5
  • Question 2

Which of the following fractions represents 12 out of 18?

CORRECT ANSWER
12/18
2/3
4/6
6/9
EDDIE SAYS
Let's start by writing these amounts as an unsimplified fraction: 12/18 We now need to consider which of the options provided are equivalents. To do this, we need to use our knowledge of times tables. If we can divide both the numerator (top number in our fraction) and denominator (bottom number) by the same amount to reach one of these options, then they have the same value. For example:
12 ÷ 2     = 6
18 ÷ 2 9
Did you spot that four out of five of these options are equivalents to '12 out of 18'?
  • Question 3

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

CORRECT ANSWER
EDDIE SAYS
To write a number as a fraction of another, we must ensure that both numbers have the same units before we start. Otherwise we cannot compare the two amounts accurately. Not remembering this key point is where a lot of students lose marks in exams, so be careful to avoid this trap!
  • Question 4

Match each pair of amounts on the left with the correct fraction to compare them on the right. 

CORRECT ANSWER

Column A

Column B

15 as a fraction of 25
15/25
20 as a fraction of 30
20/30
40p as a fraction of 80p
40/80
4m as a fraction of 10m
4/10
EDDIE SAYS
All of these pairs of amounts are expressed in the same units, which makes life a lot easier! To express one amount as a fraction of another, we simply need to place the first amount on the top as the numerator, and the second on the bottom as the denominator.
  • Question 5

Match each verbal comparison on the left with the correct simplified fraction on the right. 

CORRECT ANSWER

Column A

Column B

15 as a fraction of 25
3/5
20 as a fraction of 30
2/3
40p as a fraction of 80p
1/2
4m as a fraction of 10m
2/5
EDDIE SAYS
All of these pairs of amounts are expressed in the same units again, so we can just put the first amount on top of the second to create our fractions. However, remember that we always want to cancel our fractions into their simplest forms. Let's work through one example together:
15 ÷ 5     = 3
25 ÷ 5 5
Can you apply this example to find the other matches here independently?
  • Question 6

What is 10 out of 20 as a fraction in its simplest form?

 

Type your answer in the form a/b without any spaces and using the / key to create your fraction bar. 

CORRECT ANSWER
1/2
EDDIE SAYS
The two amounts here are expressed without units, so there is no need to convert either before we start. Let's start by writing this as a fraction with the first amount on the top and the second on the bottom:
10
20
Now consider what the HCF is between 10 and 20, which we can divide both by. We can divide both by 10:
10 ÷ 10     = 1
20 ÷ 10 2
  • Question 7

What is 32 kg as a fraction of 80 kg?

 

Type your answer in the form a/b without any spaces and using the / key to create your fraction bar.

CORRECT ANSWER
2/5
EDDIE SAYS
The two amounts here are expressed with the same units (kg), so there is no need to convert either before we start. Let's start by writing this as a fraction with the first amount on the top and the second on the bottom:
32
80
Now consider what the HCF is between 32 and 80, which we can divide both by. We can divide both by 16:
32 ÷ 16     = 2
80 ÷ 16 5
  • Question 8

What is 30 p as a fraction of £2 in its simplest possible form?

 

Type your answer in the form a/b without any spaces and using the / key to create your fraction bar.

CORRECT ANSWER
3/20
EDDIE SAYS
The two amounts here are not expressed with the same units, so we need to start by converting them into the same format. There is 100 p in a £1, so £2 = 200 p. Now write this as a fraction with the first amount on the top and the second on the bottom:
 30 
200
Now consider what the HCF is between 200 and 30, which we can divide both by. We can divide both by 10:
 30 ÷ 10     =  3
200 ÷ 10 20
  • Question 9

For each question shown, state if the fraction given as an answer is right and in its simplest form

 

Mark each question and answer as either 'Correct' or 'Incorrect' by selecting one option for each in the table. 

CORRECT ANSWER
EDDIE SAYS
Here it is important to check if the fraction has been expressed correctly, plus if the fraction has been cancelled correctly. Let's look at one example together to see this in action. 3 as a fraction of 6:
  • Question 10

5 minutes as a fraction of 1 hr is 1/20.

 

Is this statement correct?

CORRECT ANSWER
No
EDDIE SAYS
The two amounts here are not expressed with the same units, so we need to start by converting them into the same format. There is 60 minutes in an hour, so 1 hr = 60 m. Now write this as a fraction with the first amount on the top and the second on the bottom:
3    = 3 ÷ 3    =  1
6 6 ÷ 6 2
 5
60
Consider what the HCF is between 60 and 5, which we can divide both by. We can divide both by 5:
 5 ÷ 5     =  1
60 ÷ 5 12
Now you can express amounts as fractions of each other and cancel these fractions into their simplest forms, with and without units of measurements.
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