If you can't do math without a calculator then how do you know that you are able to use a calculator correctly?
ShowerThoughts
Sometimes we have those little epiphanies in the shower.. sometimes they come from other places. This is a home for those epiphanies.
Or even just the basic rules of math itself? Identity rule, Inverse rules, Commutative property, Associative property, Distributive property... There's a lot of rules that prove and create stable ground for you to accept and understand PEMDAS/BODMAS.
Simply knowing one thing doesn't prove that one thing.
All of these "rules" come up when you learn order of operations and have nothing to do with "advanced math classes".
This shower thought seems grounded heavily in ignorance of math.
That's funny, I thought it was mainly grounded in ignorance of teaching (but maybe OP means that teaching math is where you can fake it most easily)