I'm having a hard time trying to understand the use of how to deal with division in simplifying.

For instance with multiplication if you had (-6n) X 3n you take the numbers and the letters seperately so -6 X 3 woudl be -18 and n X n would be n squared.

But with 3x / 12 3 divided by 12 would be 0.25 and x divided by 12 would be what? the answer given is x/4 and I can kind of see this if i think about it as a rational number and then cancel both parts by 3 to give x/4 but this is just guess work on my part as there's no mention of this in the chapter I'm working on.

Am I thinking about this right or are there some short cut rules that I'm missing?

Also in 8x / 4x with is the answer 2 and not 2x?

Thanks.