Algebraic Fractions – possibly worse than broccoli without being good for you

Oooooh. Algebraic Fractions eh?

For a self-professed maths lover, I could sit and do them all day long…but for most ‘normal’ people these are a nightmare…and they get worse.

Algebraic fractions are mostly level 7 and upwards, so an easy version could potentially pop up in the foundation paper, but they are usually always in the higher tier GCSE maths exam. Fun times right?

Well the good news is, if you do manage to get your head around them, you will pick up a good chunk of marks.

So let’s get into it and see if we can make this topic slightly more bearable.

Before you dive in with algebraic fractions you need to make sure you are 100% confident with normal fractions and how they work.

For example:

\[\frac{12}{24}\ =\ \frac{6\ x\ 2}{6\ x\ 4}\ \]

So you can cancel the sixes. because they are being multiplied on both top and bottom.

However, a fraction like this:

\[\frac{3+3}{4+3}\ is\ \frac{6}{7\ }\ it\ does\ not\ equal\ \frac{3}{4}\]

You cannot cancel out the threes, because they are being added.

Its the same with algebraic fractions. They just look scarier and confusing because of all the letters, but the rules are the same.

Let’s have a look at a couple of examples – these are from the fat CGP AQA GCSE maths textbook, page 85.

\[\frac{3x^2y^4}{21xy}\]

We can rewrite that as:

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