# The best way to multiply!

by Domino83
Tags: multiply
 P: 1 I've got a very helpfull system for making calculations, more exactly: multiplying. How do you calculate large multiplications like e.g. 1538x483 Takes some time, isn't it? Well, I found this system for solving the problem and it's great. Whatch this, amazing: http://www.metacafe.com/watch/308408...iplying.%20Don Greetz Domino Edit: I see it has been removed today... strange.
 Mentor P: 7,272 What I see is just a complexification of normal multiplication. Whats the point?
 P: 223 I'm sorry, but this is pretty stupid ... This is merely obfuscation of the normal polynomial time, grade-school multiplication. If you want some "amazing" systems for mulitplying large numbers, look up the divide-and-conquer selection algorithm, or Fast Fourier Transforms. Or, for a system that is doable by hand use the system Al Khwarizmi discovered, one that is used today in some European countries. It works by synthesizing a binary-styled multiplication. You multiply and divide number a and number b, respectively, by 2, then strike out the even rows and add up column b. I won't bother showing how it works, because this is utterly pointless. The point being, that the technique outlined in that video is nothing but a rewrite of the grade-school algorithm, and nowhere near "the best way to multiply large numbers".
HW Helper
P: 1,007

## The best way to multiply!

I like to use the FOIL method for multiplication of 2 or 3 digit numbers, e.g.

79x91=(80-1)(90+1)=7200+80-90-1=7189

which is not very fast, but I don't care to memorize much of my times table, so it helps me.
Emeritus
PF Gold
P: 11,154
 Quote by benorin I like to use the FOIL method for multiplication of 2 or 3 digit numbers, e.g. 79x91=(80-1)(90+1)=7200+80-90-1=7189 which is not very fast, but I don't care to memorize much of my times table, so it helps me.
I would have done that same product a little differently (I find it hard to store 3 or 4 numbers in my head at a time and retrieve them later):

$$79\times 91=(85-6)(85+6)=85^2-6^2=7225-36=7189$$

Different strokes!
 P: 10 Hi - I didn't see the original (removed) link, but suggest you check out a famous book called Figuring by Shakuntala Devi. All the above methods are just basic examples of the Vedic system she resuscitated. Older members may remember she's the prodigy whose mental arithmetic beat the calculator on Blue Peter! My favourite is squaring two-digit numbers ending in 5: eg 75 squared. You just take the first number, 7 in this case, and add 1, getting 8; multiply these together, giving 56; stick 25 on the end to give 5625, the answer. Amaze your friends! The general methods allow multiplication of long numbers with the answer on the line below! eg (deliberately simple example) 3 1 2 1 2 1 37752 Working from left to right: (3x1) 3 (3x2 + 1x1) 7 (3x1 + 1x2 + 2x1) 7 (1x1 + 2x2) 5 (2x1) 2 Check it out, it's seriously quick! Best wishes x=7

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