Base rates and calculating crosses

Hello all,
I’m looking for a bit of help with rate calculations. I’ve worked in FX for a few years and I was recently asked a question which I was unable to answer. How do you know when to divide or multiply to get the rate.
I’ve never been taught this myself but having done it for a few years I know what the rates are, for instance GBP/JPY I know to multiply cable and USD/JPY to get the rate. I’m guessing that there must be a basic underlying rule but it continues to elude me!
Another question is how you know which is the base currency in an unusual currency pair, like CAD/CHF, how do you know what the market convention is?
Any help would be greatly appreciated.

to answer your first question - it’s the same as multiplying fractions, basic grade-6 algebra or math. A/B x C/D = (AxC) / (BxD), and similarly A/B x B/C, the B cancel out so you have A/C.

to answer your second question - the A of A/B is always the base, and the B is always the counter. always.

to ask my own question - how did you get through WORKING in forex for SEVERAL YEARS without knowing these basic things!?!?!?