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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:
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We also know that when we are multiplying fractions, we multiply the denominators and multiply the numerators so we can also say that:
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We should also be able to say that 2/2 = 1 and multiplying by 1 can be ignored. so now we can say that:
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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:
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Anything that is the same on the top and bottom can now cancel each other out:
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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:
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Anything that is the same on the top and bottom can now cancel each other out:
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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?
