Peasant Multiplication Article Index for
Peasant 		Shopping
Multiplication 		 

Information About

Peasant Multiplication
SHOPPER'S DELIGHT
 
Shop For:  
Department
Price Minimum:
Price Maximum:
      



Peasant multiplication, also known as '''Russian peasant multiplication''', is an old Algorithm for Multiplication . It requires no use of a Multiplication Table other than the ability to multiply by two; it also requires that the user be able to Divide By 2 , and to Add .

  • Write the two numbers (A and B) you wish to multiply, each at the head of a column.

  • Starting with A, divide by 2, discarding any fractions, until there is nothing left to divide. Write the series of results under A.

  • Starting with B, keep doubling until you have doubled it as many times as you divided the first number. Write the series of results under B.

  • Add up all the numbers in the B-column that are next to an odd number in the A-column. This gives you the result.


Example: 27 times 82



The method works because multiplication is Distributive , so:


\begin{matrix}
82 imes 27 & = & 82 imes (1 imes 2^0 + 1 imes 2^1 + 0 imes 2^2 + 1 imes 2^3 + 1 imes 2^4)\
\ & = & 82 imes (1 + 2 + 8 + 16)\
\ & = & (82 + 164 + 656 + 1312)\
\ & = & 2214
\end{matrix}


This method was known to ancient Egyptians as
mediation and duplation, where '''mediation''' means
halving one number and '''duplation''' means
doubling the other number. It is still used by peasants in some areas, such as Russia .


SEE ALSO



EXTERNAL LINKS