# Cancelling Fractions

You must have some basic knowledge of indices and factorising quadratics because this won’t be explained in detail here.

## Simplifying a Fraction

In this section we shall look at simplifying fractions by cancelling out similar factors in the denominator. The following examples deal with simplifying fractions.

^{3}n

^{2}/5m

^{2}n

To see exactly how this is simplified we’re going to work out the entire expression in parts by expanding it, for example we shall write m^{3} as

^{3}= m×m×m

Here is the expression expanded.

Since this is division we’re going to cancel the values at the top with the ones at the bottom as follows as shown below;

The ms and ns in the denominator have all disappeared. so we rewrite the expression as;

The expression can be simplified further. 30 divided by 5 gives 6.

## Factorising and simplifying

In this article we shall look at factorising and simplifying fractions.

^{2}

^{2}

^{2}

^{2}

You might be attempted here to cancel out as we did before. That would be wrong. The 8 in the numerator is not a multiple of a It is an addition. Therefore we can’t cancel.

What we will need to do is factorise the numerator first.

^{2}

Now we can do some cancelling in the fraction. If you look at the expression you will see that both the numerator and the denominator have a factor of 9, so we can cancel them out.

^{2}

Therefore the expression becomes;

^{2}

^{2}/6a

^{1}

_{3}

First we factorise the numerator as we did before

The numerator and the denominator both have a factor of **a**, so we can cancel out this in the fraction.

Both the numerator and denominator also have a common factor of 2 so we divide the numerator and denominator by 2 to cancel this out as follows;

^{1}

_{3}

This calculaton resuts in a simplified version;

Each term in the original fraction expression had a multiple of 2 and a, therefore we have divided each term by 2a to get a simplified fraction.

## Quadratic Fractions

This is example we shall explore fractions involving quadratic expressions.

^{2}+ 5x + 6

^{2}+ 5x + 6

The same principle and methods applies with quadratic expressions. Expect you have to watch out for factorisation before moving forward with the factorisation.

^{2}+ 5x + 6

The denominator needs to be factorised. Maybe there will be factors in the numerator that match with the denominator.

The common factor in both the numerator and denominator is a (x+3), we can cancel these out.

This should provide a simplified fraction of the original fraction;

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