Fast Multiplication

[Unicyclist]

I found http://www.metacafe.com/watch/315070/cool_math_trick_really_fast_multiplication/" video tutorial about a week ago and got hooked on the method. It's really simple once you get into it and works wonders. It can be easily extended to bigger numbers as well. I can't understand why they don't teach this at school.

Now, do you know any other fast calculation methods? I want to learn them all and become as calculator-independent as possible(yeah, I know).

 

[CRGreathouse]

Basic algebra gives a host of useful identities. (x+k) * (x-k) = x^2 - k^2, as an example, so you have things like 42 * 38 = 40^2 - 2^2 = 1600 - 4 = 1596.

 

[Alkatran]

The average person can't do that many additions in their head. I doubt many could even do the 3-digits case without at least writing the sums down.

In fact, all he's doing is slightly modifying the usual multiplication so you avoid writing down the sums as you go along.

 

[Gib Z]

Far too complicating. Easier to just do it the normal way, or look for other Shortcuts like CRGreathouse mentioned.

 

[Eighty]

There's the Karatsuba algorithm, but you wouldn't use that for mental calculation. :)

 

[CellarDoor]

The average person can't do that many additions in their head. I doubt many could even do the 3-digits case without at least writing the sums down.

In fact, all he's doing is slightly modifying the usual multiplication so you avoid writing down the sums as you go along.

True, it is a slightly altered version. But he's given us a swifter method, especially for the more apt mental calculators. And hey, anyone can become fast at mental calculation given time, practise and greater usage.

I prefer his method in sweeping through the calculation rather than writing each product of the numbers and then adding it, all messily on paper. By 'sweeping', I mean it's like a single thought process that doesn't involve too many steps that require memory, or the pen and paper. Although the method for larger numbers could be prone to more delicate errors.

I think it's pretty cool though, and it shouldn't be as complicated once the method is mastered and our mental abilities to calculate improve...

 

[Unicyclist]

The average person can't do that many additions in their head. I doubt many could even do the 3-digits case without at least writing the sums down.

In fact, all he's doing is slightly modifying the usual multiplication so you avoid writing down the sums as you go along.

All it takes is a tad of practice. I can do the 3-digit ones in about 7 seconds now and I'm getting the 4-digit ones pretty good as well. All in a week. I'm not a maths genius, either.

You really have to start off slowly and work your way up, then it sort of becomes automatical.

 

[complexPHILOSOPHY]

I don't like doing any calculations in my head, not that I can't, just that I prefer to write them down. The only mistakes I ever really make, is either arithmetic (forgetting to change the sign or something stupid) or writing the numbers down wrong.

If I do things in my head, I have to spend more time going back over what I just did, to make sure I had the right numbers. If I write it on paper, I can just glance at that.

I'd rather focus on problem-solving than becoming a human calculator but I also really enjoy pure mathematics and I don't have much interest in performing applied calculations. In that respect, however, I believe I am in the minority, this is a physics forum after all!

A calculation automaton is not something that I aspire to become. <3

 

[Crosson]

I don't have much interest in performing applied calculations.

In this day of computers, anyone who is interested in calculations should see it as a hobby, not a practical skill.

 

[radou]

I'd rather focus on problem-solving than becoming a human calculator but I also really enjoy pure mathematics and I don't have much interest in performing applied calculations. In that respect, however, I believe I am in the minority, this is a physics forum after all!

The minority, as you see it, is actually the majority, so you're not in the minority.