Loading please wait

The smart way to improve grades

Comprehensive & curriculum aligned

Try an activity or get started for free

Simplify Algebraic Fractions

In this worksheet, students will simplify and solve algebraic fractions using factorisation.

'Simplify Algebraic Fractions' worksheet

Key stage:  KS 4

Year:  GCSE

GCSE Subjects:   Maths

GCSE Boards:   Pearson Edexcel, OCR, Eduqas, AQA,

Curriculum topic:   Number, Algebra

Curriculum subtopic:   Structure and Calculation Algebraic Expressions

Difficulty level:  

Worksheet Overview

You may know how to simplify fractions by dividing by the same number, but do you understand why this works?

 

Let's look at an example:

If you were asked to cancel 6/8, you would divide by 2 and get 3/4.

Awesome and perfectly fine, but let's dig a bit deeper.

 

We can rewrite 6/8 like this:

6
8
=
3 x 2
4 x 2

 

We also know that when we are multiplying fractions, we multiply the denominators and multiply the numerators so we can also say that:

3 x 2
4 x 2
=
3
4
x
2
2

 

We should also be able to say that 2/2 = 1 and multiplying by 1 can be ignored. so now we can say that:

6
8
=
3
4

 

Why is this important?

You would never be asked to show all this working if you were cancelling down a fraction like 6/8 so why is this important?

It's because the technique shown, which is called cancelling by factorisation, is the only way to cancel fractions that involve algebra.

 

How to cancel by factorisation:

Whenever you see a fraction involving algebra, remember that you have to factorise it first.

e.g. Simplify the following fraction:

6x + 3
10x + 5

 

If we look at each line individually:

6x + 3 can be factorised to 3 (2x + 1)

10x + 5 can be factorised to 5 (2x + 1)

 

So we can rewrite our fraction as:

6x + 3
10x + 5
=
3 (2x + 1)
5 (2x + 1)

 

Anything that is the same on the top and bottom can now cancel each other out:

3 (2x + 1)
5 (2x + 1)
=
3
5

 

e.g. Simplify the following fraction:

15x2 + 5x
30x + 10

 

If we look at each line individually:

15x2 + 5x can be factorised to 5x (3x + 1)

30x + 10 can be factorised to 10 (3x + 1)

 

So we can rewrite our fraction as:

15x2 + 5x
30x + 10
=
5x (3x + 1)
10 (3x + 1)

 

Anything that is the same on the top and bottom can now cancel each other out:

5x (3x + 1)
210 (3x + 1)
=
x
2

 

In this activity, you will simplify and solve algebraic fractions using a deeper understanding of dividing fractions to simplify as shown in the examples above.

 

Want a bit more help with this before you begin? Why not watch this short video?

What is EdPlace?

We're your National Curriculum aligned online education content provider helping each child succeed in English, maths and science from year 1 to GCSE. With an EdPlace account you’ll be able to track and measure progress, helping each child achieve their best. We build confidence and attainment by personalising each child’s learning at a level that suits them.

Get started
laptop

Try an activity or get started for free

  • National Tutoring Awards 2023 Shortlisted / Parents
    National Tutoring Awards 2023 Shortlisted
  • Private-Tutoring-WINNER-EducationInvestor-Awards / Parents
    Winner - Private Tutoring
  • Bett Awards Finalist / Parents
    Finalist
  • Winner - Best for Home Learning / Parents
    Winner - Best for Home Learning / Parents