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Cancel Fractions when Multiplying

In this worksheet, students will practise cancelling fractions in multiplications sums so that the numbers are lower and, therefore, easier to calculate with.

'Cancel Fractions when Multiplying' worksheet

Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   Pearson Edexcel, OCR, Eduqas, AQA

Curriculum topic:   Number, Fractions, Decimals and Percentages

Curriculum subtopic:   Structure and Calculation, Fractions

Difficulty level:  

Worksheet Overview

QUESTION 1 of 10

Simplifying is one of the most useful skills when working with fractions.

It can make the numbers in our fractions much easier to deal with.

 

 

When cancelling a fraction:

You need to find the highest or greatest common factor (HCF) of the two numbers and then divide both the numerator and denominator by this.

 

e.g. Cancel the fraction:

48
60

 

For this, we need to find the largest number you can divide both 48 and 60 by.

In this case, it's 12.

48
60
=
48 ÷ 12
60 ÷ 12
=
4
5

 

 

Cancelling when multiplying:

This situation is a bit harder to get your head around.

Without going into the reasons too deeply, we can cancel fractions before we multiply them by looking for common factors in the numbers.

This means we need to find a number we can divide two (of the four) numbers by, where one of the numbers is a denominator and one is a denominator.

 

Huh? Sounds tricky?

Let's look at a few examples to clarify.

 

e.g. Calculate: 

3
4
x
5
9

 

You should notice here that there is 3 on the top of the left-hand fraction and a 9 on the bottom of the right-hand one.

This means we can divide both of these numbers by 3 and we will still get the same answer when we multiply the fractions.

31
4
x
5 = 1 x 5 = 5
93 4 3 12

 

 

e.g. Calculate:

1
2
x
4
5

 

You should notice here that there is a 2 on the bottom of the left-hand fraction and a 4 on the top of the right-hand one.

This means we can divide both of these by 2 and still get the same answer when we multiply the fractions.

1
21
x
42 = 1 x 2 = 2
5 1 5 5

 

 

Are these the only scenarios to be aware of?

There could be a combination of both the examples we have shown you.

Don't forget that you could also cancel a fraction if the numerator and the denominator have a common factor within the same fraction.

 

 

 

In this activity, you will practise applying the process shown above to cancel fractions in multiplications sums so that the numbers are lower and, therefore, easier to calculate with. 

Complete the sentence below to summarise the rule when simplifying single fractions. 

There are some key rules we must remember when simplifying fractions.

 

Can you remember what we should do in the situation below?

Write 24/60 as a fraction in its simplest form.

 

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

What is the most useful common factor in the calculation below?

 

3
4
x
1
9

 

Which of the numbers in the list are common factors for the multiplication below?

 

3
4
x
2
9
1

2

3

4

9

Simplify this sum:

 

2
7
x
7
11

 

...into the form:

 

a
b
x
c
d

 

Then pair the numbers and letters below together. 

 

Column A

Column B

a
2
b
1
c
11
d
1

Simplify this sum:

 

2
3
x
6
14

 

...into the form:

 

a
b
x
c
d

 

Then pair the numbers and letters below together. 

 

Column A

Column B

a
2
b
1
c
7
d
1

Match the original multiplication sums on the left to the simplified versions on the right. 

Column A

Column B

3/7 x 14/16
3/1 x 1/8
5/9 x 6/20
1/3 x 2/5
2/9 x 6/10
1/3 x 2/4

Which of the options in the list are simplified versions of the equation below?

 

12
18
x
9
15
4
18
x
9
5

12
2
x
1
15

2
1
x
1
5

2
5
   

Using your knowledge of simplifying, find the answer to:

 

3
4
X
8
10
X
5
9

 

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

 

Your answer should be in its simplest possible form. 

  • Question 1

Complete the sentence below to summarise the rule when simplifying single fractions. 

CORRECT ANSWER
EDDIE SAYS
Remember that if you are dealing with a single fraction, we're looking for the highest or greatest common factor. Common factors in general are helpful, but finding the HCF will mean that you reach the simplest possible answer quickest. Remember this fact in the remaining challenges in this activity.
  • Question 2

There are some key rules we must remember when simplifying fractions.

 

Can you remember what we should do in the situation below?

CORRECT ANSWER
EDDIE SAYS
When you are multiplying, you aren't looking for just one number to divide by, you are looking for pairs of common factors. Whichever number you choose to simplify by, both the denominator and the numerator must be able to be divided by this.
  • Question 3

Write 24/60 as a fraction in its simplest form.

 

Give 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
We need to find the HCF of both the numerator and denominator here. Which numbers can divide 24 and 60 by? 1, 2, 3, 4, 6, 12 Which is the highest of these numbers? 12 Divide both the numerator and denominator by 12 to reach our simplified fraction. 24 ÷ 12 = 2 60 ÷ 12 = 5 So the overall answer is 2/5.
  • Question 4

What is the most useful common factor in the calculation below?

 

3
4
x
1
9

 

CORRECT ANSWER
3
EDDIE SAYS
We have a 3 in the left-hand numerator and a 9 in the right-hand denominator. They are both divisible by 3, so we have a common factor of 3. Top tip: When you see a 1 in either fraction, you can assume that it will be of limited use to focus on this as it can never be divided any lower than it currently is.
  • Question 5

Which of the numbers in the list are common factors for the multiplication below?

 

3
4
x
2
9
CORRECT ANSWER
1
2
3
EDDIE SAYS
1, 2 and 3 are all common factors. 1 doesn't help us with this sum, or in fact any sum, as it can never be simplified further. 2 is a common factor between 2 and 4, whilst 3 is a common factor between 3 and 9. Can you use these facts to work out the answer to this sum?
  • Question 6

Simplify this sum:

 

2
7
x
7
11

 

...into the form:

 

a
b
x
c
d

 

Then pair the numbers and letters below together. 

 

CORRECT ANSWER

Column A

Column B

a
2
b
1
c
1
d
11
EDDIE SAYS
The only common factor we have in the original sum is 7. We can therefore convert both of the 7s in these fractions into 1s instead. If we divide both of these fractions by 7, we get: 2/1 x 1/11 Did you match those letters and numbers up accurately to show this?
  • Question 7

Simplify this sum:

 

2
3
x
6
14

 

...into the form:

 

a
b
x
c
d

 

Then pair the numbers and letters below together. 

 

CORRECT ANSWER

Column A

Column B

a
1
b
1
c
2
d
7
EDDIE SAYS
We have two common factors here: 3 and 2. So we can divide the 2 and 14 by 2, then the 3 and 6 by 3. If we do this, we reach: 1/1 x 2/7
  • Question 8

Match the original multiplication sums on the left to the simplified versions on the right. 

CORRECT ANSWER

Column A

Column B

3/7 x 14/16
3/1 x 1/8
5/9 x 6/20
1/3 x 2/4
2/9 x 6/10
1/3 x 2/5
EDDIE SAYS
Just remember that you need to spot the common factors here. 3/7 x 14/16 could have a common factor of 7 which initially gives us 3/1 x 2/16. But did you notice that 2/16 can also be simplified to 1/8? 5/9 x 6/20 have common factors of 5 and 3. If we divide 5 and 20 by 5, then 6 and 9 by 3, we reach: 1/3 x 2/4 2/9 x 6/10 have common factors of 2 and 3. If we divide 2 and 10 by 2, then 6 and 9 by 3, we reach: 1/3 x 2/5 How did you get on there?
  • Question 9

Which of the options in the list are simplified versions of the equation below?

 

12
18
x
9
15
CORRECT ANSWER
4
18
x
9
5

12
2
x
1
15

2
1
x
1
5

2
5
   

EDDIE SAYS
Did you notice they were all cancelled versions? Each one has been affected by a different common factor. This illustrates the point that there are multiple ways to tackle these kinds of questions. The first option has simplified 2 numbers using the factor of 3. The second option has simplified the opposite 2 numbers using the factor of 9. The third option is a simplified version of combining the two simplifications above: 4/2 x 1/5 = 2/1 x 1/5 The fourth option is the simplified answer to the sum: 4/2 x 1/5 = 4/10 = 2/5
  • Question 10

Using your knowledge of simplifying, find the answer to:

 

3
4
X
8
10
X
5
9

 

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

 

Your answer should be in its simplest possible form. 

CORRECT ANSWER
1/3
EDDIE SAYS
This equation has a lot of common factors! Whichever factors you chose, you needed to reach:
1
1
X
1
1
X
1
3
Great work, you've completed another activity! Why not practise cancelling algebraic fractions now?
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