Many students do not understand the rules for when one can 'cancel' in regards to fractions

The first step is to assess whether there are any plus or minus signs anywhere within the fraction. If not: separate the denominator into brackets, for instance if the denominator contained 2x you would split that into (2)(x) Next: see if the numerator can be split into either of those same brackets, for instance if the numerator contained 24 you could split that into (2)(12)Next: you now have a fraction containing brackets only and two of these brackets are on both the bottom and the top of the fraction. You can therefore cancel them out - i.e. ignore them. Finally: you are now left with 12/x which is a simplified fraction.If however, the fraction does have plus or minus signs it is slightly more complicated.e.g. (4x+2)/(8x+4) I have chosen this fraction as it has addition signs on both the top and the bottom of the fraction and so is an example of one of the trickier questions one could be asked.The first step remains the same: write the denominator in brackets in this case it would become (4)(2x+1) as if you multiply those brackets together it is equal to the original denominator of 8x-4. Next: write the numerator in brackets which in this case could be (2)(2x+1). You can now see that (2x+1) appears on both the bottom and top of the fraction and as it is contained within bracket signs it can be cancelled leaving 2/42 divided by 4 can then be worked out with mental maths as 0.5 or one can write the 4 as (2)(2) and cancel the 2 from the top with one of the 2s from the bottom leaving 1/2 which is equal to 0.5