# Can't resist these fractions

15th November 2002 at 00:00
I teach GCSE physics. My pupils find it difficult to rearrange formulae when there are fractions involved. For example, in dealing with two resistors in parallel to make R the subject.

Have you any ideas to help?

Many pupils find it difficult to rearrange equations similar to this one. Though there is more one way to rearrange a formula, the problem often lies in pupils' not understanding how to add fractions.

I suggest a brief revision on the addition of fractions first.

Let us consider the sum

As the fractions have different bottom numbers (denominators), they cannot be added directly, because there are different sized chunks of a whole. One third is a bigger chunk than one fifth. To add them together it is necessary to have the denominators the same size, that is, the same number. There is a neat little trick using a kind of cross multiply that does the job nicely. I have used colour to show you what I mean (the use of colour can sometimes usefully illuminate the concept you are explaining).

We know that because multiplication by 1 leaves the value of the fractions unchanged.

A common mistake is to try and add the two denominators together, this can be avoided if the question is asked "How many 15ths?" and pupils are reminded that the denominator only tells us the size of the "chunk".

So let us apply this to be equations for two resistors in parallel.

First we have to make the denominators the same by multiplying by The next stage is to 'cross multiply', that is, to multiply the LHS by R2R1 and the RHS by R.

"Cross multiplying" is a shorthand for the mathematical process, which is to multiply both sides of the equation by R and R2R1; the actual form is shown below. Pupils can be encouraged to use "cross multiplication" but I suggest that this should be firmly grounded in the actual process so that if they forget the short cut they can tackle the problem based on understanding the process: Wendy Fortescue-Hubbard is a teacher and games inventor.Email your questions to teacher@tes.co.ukOr write to TES Teacher, Admiral House, 66-68 East Smithfield, London E1W 1BX

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