Q:

How do you multiply in your head?

I have autism so my brain is a little broken and i tend to do most things in an odd way. when i multiply numbers i tend to break them down to certain multiples for example when i multiply
$183 *274 $
$18*27 \to 20*30 \to 2*3 *100 -3*20 -2*27 *100 + 3*275 -3 +4*2*100-2*4*10 =50142$ 
of course i dont actually do the times 100 part i just shift the decimal point in my mind often ill multiply out all the numbers then re align them at the very end but for ease of you understanding what im saying i as close to approximated it in a less nonsensical way
something really easy like 
$213*712$ i would write as $3*7 +3 *712 $ in my mind then write $(49, 7 , 14)*3 $ then write $(150-3, 21, 28+14)$ then + $21, 3 ,6$ 
Then i would shift my digit  so $1470 +21\to  14910+42 \to 149520$ then $ 210+3 \to 2130+6$  lastly $520+136$ and $49+2 $ to the final number $151656$
Most examples will reduce to really simple cases like the second example ( i actually get the numbers from licence plates as im driving down the road i just multiply the first two i see together when im done i select a new 2 numbers from in front of me and repeat till i arrive at my destination.)
I didn't realize until recently that my over-counting correction was actually related to set theory $18*27 \to 20*30 \to 2*3 *100 -3*20 -2*27 *100 $ the fact that you dont subtract $2*30$ but $2*27$ for the second value is just something i knew or maybe realized that it worked from trial and error back when i was a child and have simply forgot how i came to realization that it was needed. 
Most 3 digit by 3 digit multiplications i can complete in about 15 seconds even for a difficult one in my head 3*4 maybe a little longer 4*4 depending on the difficultly the multiplication may take me over a minute at which point its faster to try and find a piece of paper or find the calculator app on my phone.
im wondering if there are other tricks or methods to multiplying large numbers in ones head that people employ that im not aware of?
i also employ a similar method for division but it requires one to memorize several prime fractions like 1/7 1/11 1/13  etc.
any tips or tricks however obscure welcome.
Also i have no idea what to tag this as.

A:

This is a field of work, lots of contribution have come in mid-20th century from Jakow Trachtenberg, and his system bears his name. You can read up on the Trachtenberg system on Wikipedia.

