Mental Math

never use paper

>>8400193
Jump off a sufficiently tall structure so you become fully paralysed neck down.

>>8400193
Learn better methods of doing the same operation. Practice serial processes until the rhythm is natural and intuitive. Favor general methods over specific ones, but don't ignore methods that work very well in specific cases.

eg
9555354354390093290888343 x 5 = ?
In a general case you just move from right to left and track carries as you do so. But more deficient in a multiplication by 5 is to just add a 0 on the end, then separate out each set digits that form even numbers, and divide by 2.
9555354|354|390|0932|90|888|34|30
4777677|177|195|0466|45|444|17|15

= 47,776,771,771,950,466,454,441,715
etc. There are a lot of methods for a lot of tasks. Have to also bear in mind which ones work best for your own neurological machinery. ie, if like me, you often have subpar working memory capacity, you might want to hold any carries in a different way, else you will lose elements of the whole.

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19KB, 657x527px

>>8400345
nerd fuck off

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1MB, 2216x2752px

>>8400649

>>8400649
>nerd fuck off
>/sci/
let me repeat that for you
>nerd fuck off
>/sci/
>in /sci/
>in matha'fakk'n /sci/

31 x 21 is the same as
(30 x 21) + (1 x 21)

I get messed up when the end values are in the middle
34 x 35
(34 x 30) + (5 x 34)

>>8400193
For addition, use a good abacus, like a soroban, for holding intermediate figures and doing addition/subtraction.
https://en.wikipedia.org/wiki/Soroban

Use slide rules: >>8398197
>If you use a slide rule enough, you also develop a visual/tactile memory of its workings.

It's the same principle: by routinely working with a simple physical object, you will develop a subconscious anticipation of its behavior. Eventually you can get the answer just by imagining using it.

Get a nice pen, do your algebraic stuff in ink, stop using scratch paper for straightforward problems (like you might get assigned in an exam), and get fussy about keeping your solutions neat and orderly. This will force you to work the problem out in your mind several steps ahead of what you write down. The further you work things out in your head, the less backtracking you'll have to do, and the neater your work will be. Erasing or throwing out your missteps conceals the untidyness of your thoughts from yourself. You want to improve, not conceal.

>>8400345

this is neat

>>8400694
Oh, and another thing: spend your time with your tools doing problems that are just a little too hard to do quickly in your head, and time without your tools doing problems that you can just barely do quickly in your head.

Learn to make up problems for yourself, and find sources of problems to practice on.

You have to work with something a lot to get good at it.

>>8400193
Look up Arthur T. Benjamin, he has some cool methods to help with crazy mental calcuations

>>8400193
Smash the left side of your head against the wall and hope you become an aquired savant.

>>8401027
Sounds sensible. Is there any literature on the subject?

>>8400649
(you)

>>8400345
>>8400947
This

>>8400193
diet i.e. don't eat too much sugar and fat

>>8400193
You want to do 2 things:
>Carry fewer terms
>Use as few steps as possible

For example
>3.24×6

I've always found it easier to subtract 0.04, then do 3.2×6 = 19.2, then do 0.04×6 =0.24, so:
>3.24×6=19.44

I'll admit that for smaller numbers you don't get much of a saving, but it gets better as the numbers get larger. Another good one is estimation, take the example here >>8400345, sure it's a neat method but I don't really see how that would help you do arithmetic, all that partitioning and division seems prone to error. Instead take the leading few terms:
>956×5
>960×5=4500+300=4800
>5×4=20
>956×5=4780

Yeah so it's not exact but it's a decent estimation, and obviously you can just hold a few more terms to get a better estimate.

>9555×5
>9555×5=95×5×100+55×5=47500+275=47775.

A much better estimate for very little extra work. When it comes to fractions we can do something like:
>32/7
>32=35-3
>32/7 = 35/7 - 3/7 = 5 - 3/7 = 5 - 0.3
>32/7 = 4.7

Which is pretty close to the actual answer. Obviously for this example you could just have calculated it explicitly, since its not that hard. But again you get better savings for larger numbers.

I find that using some combination of these I can get either the exact answer or something close to it, which is often good enough.

Thank you very much for all your replies.

>>8401452
Do these kinds of 'tricks' come naturally to some and not to others?

Anyways, I wish OP luck!