  # Simplify Algebraic Fractions

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