hi 295Ja

Here is an example where 'cross-multiplying' has been done incorrectly.

Student remembers about cross multiplying, but does it incorrectly:

It is because of this sort of mistake that teachers advise against using cross multiplication.

I prefer to teach 'multiply every term by the same amount', so in the above example:

Another thing you may find helpful is to convert the algebra to numbers.

In my example, suppose u = 3, v = 6 and f = 2

In the original:

This is correct.

In the error version:

This is NOT CORRECT so the error is revealed.

In my correct version:

This has come out correctly.

This is not a guarantee that no mistake has been made as I might just have been lucky to get the 'right answer', but it will help to confirm that what you have done is right.

It is 11.14 am in the UK.

Bob