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Cancel Fractions when Multiplying

In this worksheet, students will practise cancelling fractions when they are multiplying.

'Cancel Fractions when Multiplying' worksheet

Key stage:  KS 4

Curriculum topic:  

Curriculum subtopic:  

Difficulty level:  

Worksheet Overview

QUESTION 1 of 10

Simplifying is one of the most useful tools when dealing with fractions. It makes the numbers easier to deal with.

 

Reminder when cancelling a fraction:

When you have to cancel a fraction, you need to find the highest common factor (HCF) of the two numbers and then divide by this.

Example:

Cancel the fraction.

48
60

For this, we need to ask what the largest number you can divide both numbers by is. In this case, it's 12.

48
60
=
48 ÷ 12
60 ÷ 12
=
4
5

 

Cancelling when multiplying:

This one 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 numbers by where one of the numbers is on one of the denominators and one is on one of the denominators.

Huh? I don't get it.

Let's look at a few examples to clarify.

Example 1:

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 by 3 and we will still get the same answer when we multiply.

31
4
x
5
93

Example 2:

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.

1
21
x
42
5

 

Are these the only ones?

There could be a combination of both the ones I have shown you.

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

To cancel a single fraction we need to find the...

There are some key rules we must know, can you remember what we should do in the following situation?

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

 

Give your answer in the form a/b.

What is the common factor in the calculation below?

 

3
4
x
1
9

 

Which of the following numbers are common factors for the multiplication?

 

3
4
x
2
9

 

1

2

3

4

9

Before we do the multiplication, we could simplify this fraction...

2
7
x
7
11

...into the form

a
b
x
c
d

 

Column A

Column B

A
2
B
11
C
1
D
1

Before we do the multiplication, we could simplify the fraction...

2
3
x
6
14

...into the form

a
b
x
c
d

 

Column A

Column B

A
2
B
1
C
1
D
7

Match the uncanceled multiplications to the canceled multiplications.

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 these options 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

 

giving your answer as a fraction in it's simplest form (a/b).

 

 

  • Question 1

To cancel a single fraction we need to find the...

CORRECT ANSWER
EDDIE SAYS
Remember that if you are dealing with a single fraction, we're looking for the highest common factor. Not just a common factor!
  • Question 2

There are some key rules we must know, can you remember what we should do in the following situation?

CORRECT ANSWER
EDDIE SAYS
When you are multiplying, you aren't looking for one number to divide by, you are looking for pairs of common factors.
  • Question 3

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

 

Give your answer in the form a/b.

CORRECT ANSWER
2/5
EDDIE SAYS
We're looking for the HCF. Which number is the biggest you can divide 24 and 60 by? (12). Then, just divide both of the numbers by 12.
  • Question 4

What is the 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.
  • Question 5

Which of the following numbers are common factors for the multiplication?

 

3
4
x
2
9

 

CORRECT ANSWER
1
2
3
EDDIE SAYS
1 is a common factor but doesn't help us. The ones we need to look at are the 2 and 4 having a common factor of 2, and the 3 and 9 having a common factor of 3.
  • Question 6

Before we do the multiplication, we could simplify this fraction...

2
7
x
7
11

...into the form

a
b
x
c
d

 

CORRECT ANSWER

Column A

Column B

A
2
B
1
C
1
D
11
EDDIE SAYS
The only common factor we have here is the 7. If I divide both of these by 7, I get 2/1 x 1/11.
  • Question 7

Before we do the multiplication, we could simplify the fraction...

2
3
x
6
14

...into the form

a
b
x
c
d

 

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. If I divide my fraction by these, I get 1/1 x 2/7.
  • Question 8

Match the uncanceled multiplications to the canceled multiplications.

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. 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?
  • Question 9

Which of these options 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 just had a different factor taken out. This illustrates the point that there are multiple ways to tackle these kinds of questions.
  • Question 10

Using your knowledge of simplifying. Find the answer to...

 

3
4
X
8
10
X
5
9

 

giving your answer as a fraction in it's simplest form (a/b).

 

 

CORRECT ANSWER
1/3
EDDIE SAYS
This equation has a ton of common factors. You should have got...
1
1
X
1
1
X
1
3
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