Who else here can't do mental math & doesn't know x tabl

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Mathematically speaking (as in, repeating back what my university professor says), division isn't a real function. It exists solely as a complimentary function to multiplication, by which I mean it's just for undoing multiplication. That's why you get things like division by 0 = undefined.

Before making this turn into a mathematical discussion division is actually functional, since for every input within it's domain ( i.e. a factorial 1/x with domain ℕ \ 0 ) it has exactly one solution. Division is considered an elementary arithmetic, it is like addition, subtraction and multiplication you cannot further simplify every instance of it's functionality without using it's own definition. It is just something that you are going to have to live with, especially in later mathematics courses where divisions can become a real pain ( i.e. integrals ).

Sticking to the topic, I am not really good at simple mental mathematics but that is probably because I haven't trained in them at all. I think that is something you really have to work at to become good at it. What I do excel at is mentally visualising formulas, graphs, transformations, etc. mainly because I am a visual thinker and I am doing a lot of training in it for my degree. For a lot of things you simply have to work at it to become good at it.

The main thing that mostly hinders me at simple math is that I am uncertain of myself, to the point where I constantly find myself double checking with a calculator whenever I do mental math. It makes the whole process of mental math become rather pointless.