Math, How do you do it?

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For those of you who are gifted in math or enjoy math:
How do you do math?

When I do math it often feels similar to the way a fifteen puzzle feels.
I know how certain things have to look to get to a solution and I just move symbols around to make the math look like the solution.
I actually have no idea to show the formalisms associated with algebra, I just know what symbols look like when you move them around and what rules they follow.

eg.

x
_ = 5

2

To me I just pictorially move the 2 over and when it's beside the five and wasn't there before I know that means multiplication. so the answer is 10.
I'm just learning that the proper way to do this is by multiplying each side by 2 and then performing the appropriate functions.

What ways do you people do math?

Depends on the kind of math.

Arithmetic is very visual for me, picturing the manipulation of the digits and bringing together the results.

Algebra is visual in a different way, usually representations of polynomial graphs.

Algebraic structures look like lattices in my head; countable sets look like zippers; etc.

I could go on and on. Suffice it to say, it's heavily visual.

With numbers

Numbers have shapes. I manipulate the shapes to get the answer. Multiplication means cutting or stretching; addition or subtraction means stacking.

I do algebra the same way the OP does it, by "moving" numbers around.

Most of the time, I don't. My brain does it for me. When I was doing math at school, every now and then it would work out something apparently amazing that would shock everyone, but half the time I would have no idea to work anything out step-by-step. Geometric math was my specialty. I would just usually stare at the question, and my brain would tell me the answer (after varying amounts of time). I didn't really pursue this talent, firstly because I have no idea how I would do that, and secondly because I don't like math.

Oh my god I'm so terrible at math. I just count one by one usually.;;;;
But the way you do it sounds cool. I feel like I should be able to do it like that, because that's similar to how I solve other problems, but it's just not there. My math section is blank.;;;

these replies are really cool, keep them comming

I'm afraid math is quite beyond me. I still count with my fingers.

How do I do it? Calculators mostly or flicking to the back of the book where the answers are.

This is how I do fractions. 3/5 is a chocolate bar with 5 pieces of chocolate. If you take 3 of the chocolate pieces you got 3/5 of the chocolate bar. Graphs are a great way of solving problems I use them a lot. Also you can understand better some math concepts like the lagrangian or linear programing through graphs.

I would say that it is some admixture of the methods posted by Noxide, Callista and Visagrunt mentioned.

To quote Rainman;

'I just see it.'


I guess that would make it visual.

I figured recently that my biggest strategy is halving and doubleing easily, such as for when I do 5 times, I halve and then times by ten, sounds complicated, but for me I can double and halve simple numbers quite easily. I also turn the numbers into fractured blocks in my head when I imagine them into fractions. I can be pretty good, though I still get mistakes at times due to my thinking being flawed on not easily tranlateable to others. I also have a weired thing where if I close my eyes and lift my head a little bit for some reason my calculative and focus ability increases and I can do things faster, looks strange to others though.