Russian Peasant MultiplicationDate: 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/ |
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