Russian Peasant Multiplication

Date: 08/19/97 at 14:40:52
From: S.Nickless
Subject: Question for dr.Math

I'm a pupil at Archbishop Ilsely Secondary School in England and 
have a maths project to do. The project is on "russian" or "peasant"
multiplication. I have to investigate this and my research on the Web 
has hardly turned up anything. I really need some help so if you could 
give me any pointers and what are the appropriate formula and
equations I would be really grateful. 

Thanks, Daniel Nickless

Date: 08/19/97 at 15:45:04
From: Doctor Sarah
Subject: Re: Question for dr.Math

Hi Daniel -

Here's an explanation from the Explorer site.

 http://explorer.scrtec.org/explorer/explorer-db/html/806787711-81ED7D49.html   

The so-called "Russian Peasant Method of Multiplication" is based on 
the binary system. There are said to be places in Africa where this 
method is still used.

To multiply 92 x 37, write 92 at the top of one column and 37 at the 
top of another.  Divide 92 by 2 and multiply 37 by 2, writing the 
results below the original numbers.

   92   x    37           
  *46        74           
  *23       148     148     
  *11       296     296     
    5       592     592 
    2      1184           
    1      2368    2368  
                   ----   
                   3404     
                          

Continue to divide by 2 in the first column and to multiply by 2 in 
the second column.

When an odd number is divided by 2, disregard the remainder. Stop when 
1 is reached in the first column and all the numbers represented in 
the second column are opposite representations of odd numbers in the 
first column. The correct answer is 3404.

After practicing with many problems, try to determine where this 
method of multiplication is related to the binary system. 

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