B How can you do e.g. 756 x 675 mentally?

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Hello!

How can you do e.g. 756 x 675 mentally?

Any good trick?
 

hilbert2

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Hello!

How can you do e.g. 756 x 675 mentally?

Any good trick?
To do that, you need a very good short-term memory to not lose track of what you're doing.

Something like ##999\cdot 999## is simpler because then

##(1000-1)^2 = 1000^2 + 2\cdot 1000 \cdot (-1) + (-1)^2 = 998001##

and the numbers here are "special" enough to easily keep track of.
 
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Vedic math might have some tricks to allow you to do this too but I think the Trachtenberg method is the best mentally.

https://vedicmathsindia.org/vedic-mathematics/?v=7516fd43adaa

I need to say that Vedic math is not without controversy as the name is a misnomer (ie not from the Vedic period but from a 1965 book on the subject) and its more a collection of arithmetic tricks and not math perse.

As a kid, when I was asked to do this kind of calculation by a friend, I'd ask him why he needed the answer and while he was responding, work it out mentally and then answer. It gave me a few moments but people thought my answer came out instantaneously which was okay by me.
 
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and the numbers here are "special" enough to easily keep track of.
756*675 luckily has special enough numbers. 4*675=2700, and 756 happens to be divisible by 4. So simplifies to 189*27.
And 189 is 200-11. 11*27 is nicely 297. So 5400-297=5103. The answer is 510300.
 

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