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Ah. Hmmm. I mean, division is just multiplication turned on its head, so maybe it would help to start with how you visualise multiplication, and see whether you can extend that to work for division too? ๐คทโโ๏ธ
If it makes you feel any better, my arithmetic is horrendous. I understand complex mathematical concepts easily, but don't ask me to add 2 big numbers. It's ridiculous ๐
you know cuisenaire rods? those counting stick things. i think in those. that means addition makes a line, multiplication makes a plane, exponentiation makes a cube. higher exponents make cubes of cubes.
division doesn't really fit in that visual because it's a quantised system. fractional multiplication fails for the same reason.
Division is taking a plane and breaking it into equal lines. I assume when you multiply you are already giving that plane bounds because anything else wouldn't give you a result. It takes a few passes to go the other way, but your facility with powers of two can help you narrow it down quickly enough. You're just trying to find out how long the box of a certain width has to be to fit a given number of blocks.
Maybe it helps, maybe it doesn't. It's surprising how many ways people have found to achieve the same goal.
yeah i understand the principle, but the issue is i have to "go through the motions" every time. i can't do a quick ballpark for division in the same way as for other arithmetics so i can't self-correct.
I'm not sure if that's a familiarity issue or an intuitiveness issue. I'd say I'm very good at math, but I'm also weakest at division mentally. I think part of it is we come across the other operations more frequently in life and our brains are more tuned for them, whether that be nature or nurture. I think the only way to change that is practice.
the question is where to start practising. i am absolutely terrible at most math; i can't balance an equation to save my life, i tend to get all my trig backwards, and the only thing i consistently get right for calculus is that odd-power exponentials are assymmetrical. despite that i struggled my way up to differential equations and found that annoyingly, combinatorics and boolean algebra came naturally.
you are describing my experience with math almost 1:1, it's uncanny... division is unintuitive, i've re-learned calculus from scratch like four times during my school career and none of the actual math made intuitive sense, trig never clicked. i've been doing computer graphics for like 6 years now and despite trig being everywhere i still need like 30 seconds to puzzle out what
sin(0)is for the thousandth time. but i aced combinatorics without even trying as soon as i heard that the funny fraction-looking thing with parentheses is called "n-choose-k", and if you give me a boolean expression with 5 levels of nested parenthesis and i can simplify it in my head in seconds.i know, right?! like, a friend of mine was doing a homebrew computer project a year or so ago and had issue with some complex instruction logic in the alu or whatever, and without having done it for over a decade i just sketched up a karnaugh map and struck two terms out. i even confused myself with that one.