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Simplify Algebraic Fractions

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

'Simplify Algebraic Fractions' worksheet

Key stage:  KS 4

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

QUESTION 1 of 10

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.

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