What's the Algorithm Behind This Easy Mental Multiplication Trick?

[abdo375]

Amazing, does anyone know the algorithm behind this?
http://www.metacafe.com/watch/296904/easy_mental_multiplication_trick/"

 

[Office_Shredder]

Basically, because of where the tens and the ones intersect, you get one corner as the hundreds (ten*ten), two corners are tens (1*10, 10*1), and one corner is the singles (1*1)

I only watched the first example, obviously you could expand it to hundreds and thousands and such

 

[dontdisturbmycircles]

That's kind of neat.

 

[theCandyman]

Very nice, I will have to show that to my younger siblings. Thanks for sharing the link.

 

[moose]

(10 + 2)(20 + 1)
10 * 20 + 10 * 1 + 2 * 20 * 2 * 1
Doing the trick does the same thing as multiplying that out the way you would with variables in there. (you know, like if it
were (x + 1)(x - 5) or something and you wanted to expand it)

EDIT: That is if this is the trick I'm thinking of.

 

[Office_Shredder]

moose, that's basically what it does

 

[Jimmy Snyder]

If this method helps you, then go for it. However, it has its limitations. Try this one the traditional way and the graphical way:

999 X 999

 

[Alkatran]

It's an interesting way to multiply numbers, but equivalent to just summing the product of all the digit pairs. Frankly, drawing the picture is just slowing him down. Very creative though, don't think I would have thought of doing it.

Hey, we should come up with other ways to do math using pictures.

 

[moose]

I like the trick that you can use to square numbers. Let's say you want to square 28... You know that 30*30 = 900.

If you then use the derivative of x^2 to approximate it, you subtract 2*30*(30-28), resulting in 780. Then as a correction, you add in the change squared (30-28)^2, so your answer is 784. This is really simple around 50, because you just subtract or add 100s.

So if you want to find x^2, and know y^2
x^2 = y^2 - 2y(y - x) + (y - x)^2

Really fast and easy to do. I would think that most people on this board already know of this "trick" though.

 

[Cyrus]

Wow, that's pretty neat.

Here is an even neater trick!

http://www.shiar.org/ticalcs/ticlxpix/ti83+01.gif