# Cancelling Fractions

This is another entry that shows how to work with fractions. Cancelling fractions is a big part in mathematics especially when simplifying the fractions. Here we shall be looking at how to simplify fractions by cancelling the common factors and factorising to identify common factors. You must have some basic knowledge of indices and factorising quadratics because I won’t explain any of this here.

## Simplifying a Fraction

Here we have a fraction that we would like to simplify. To see exactly how this is simplified we’re going to work out the all expression in parts for example we shall write m^{3}= mxmxm Since this is division we’re going to cancel the values at the top with the ones at the bottom as follows; We can see that all the**n**valuables have disappeared and the**m**at the bottom have all disappeared, so we rewrite the expression as; Now we need to simplify the expression further. 30 divided by 5 gives 6 so our simplified expression becomes.## Factorising and simplifying

Here is an example that we’re going to attempt to simplify but we will have to factorise first. Simplify the fraction; 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. 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 3, so we can cancel them out. Now the expression becomes; This is the simplified version of the original expression. Each term in the original expression was a multiple of 3. What we did was divide each term in the expression by 3 to get a simplified version of the fraction.## Example

Here is another example of a fraction to simplify. Simplify the fraction; 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 fraction. Both the numerator and denominator also have a common factor of 2 so we divide the numerator and denominator by 2 to cancel as follows; What remains is the simplified version; As you’ve seen each term in the original fraction expression had a multiple of 2 and of a. We have divided each term by**2a**to get a simplified fraction.## Quadratic Fractions

The same principle applies with quadratic expressions; Here we need to factorise the denominator instead. The common factor in both the numerator and denominator is a (x+3), we can cancel these out. What remains is the simplified fraction of the original fraction;## Useful Links

Learn more about this topic in the following pages.

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