Russian Peasant Multiplication

Date: 11/01/97 at 19:07:59
From: Karl Gabzdyl
Subject: Russian peasant multiplication

Dear Dr. Math,

Could you please tell us what Russian peasant multiplication is?  

The parent of a gifted 4th grader.

With great respect,
Karl A. Gabzdyl

Date: 11/05/97 at 14:59:04
From: Doctor Terrel
Subject: Re: Russian peasant multiplication

Dear Karl,

The Russian Peasant multiplication idea is rather interesting, as it 
only involves multiplying by 2 (doubling) and dividing by 2 (halving), 
and, of course, ordinary addition. It goes something like this:

Let's say we wish to multiply 27 by 56.

We write our work as follows...

   27    56    In the first column I double as I go down.
   54    28    In the 2nd column, I halve my numbers, throwing
  108    14       away any remainder of "1" I might obtain.
  216#    7*   Notice I've indicated the odd numbers by
  432#    3*   an asterisk " * ".  And the corresponding
  864#    1*   numbers in the other column by the symbol 
               " # ". 

Now my desired product for 27 x 56 will be the sum of the numbers 
indicated by the #-symbol.  This is 216 + 432 + 864 = 1512.

Now you might ask: what would happen if I reversed my columns?  Well, 
as you know 27 x 56 = 56 x 27 [the commutative property], we should 
get the same product.  Let's see..

  56#   27*
 112#   13*
 224     6
 448#    3*
 896#    1*  

This time we have 56 + 112 + 448 + 896 = 1512.  

-Doctor Terrel,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/