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Re: Russian Peasant Multiplication: Explained!
Posted:
Mar 3, 1998 9:26 PM


This article is essentially a duplication. However using your example, I can now make my previous explanation even simpler.
In article <34FCB257.2C7DF882@ufl.edu>, Kevin Fortin <kfortin@ufl.edu> wrote: >Thanks to the sci.math readers whose responses helped me to understand >"Russian Peasant Multiplication"! > >Here's my own attempt to explain it: > >[Please use a nonproportional font so the columns line up. Also, I >SNIP< >Example: 19 x 54 = X > >(H = "halving column", D = "doubling column"; in column H, any remainder >is discarded after each halving.) > >_H_ _D_ >54 19 (ignored) >27 38 >13 76 > 6 152 (ignored) > 3 304 > 1 608 > >The even numbers in column H are crossed out, along with the >corresponding entries in column D across the way. The remaining numbers >in column D are added up to give the product: >19 x 54 = (38 + 76 + 304 + 608) = 1026
Now, as I explained in my previous article, all you need to do to explain this is notice that when the lefthand column is even, the product of the two columns remains the same when you move down to the next line. (For instance, 54 * 19 = 27 * 38.) However when the lefthand column is odd, this is not quite correct. The discrepancy is in fact the number in the righthand column. (For instance, 27 * 38 = 13 * 76 + 38.) Now if you take the final entry in the righthand column and add to it all the discrepancies, i.e. all the other entries in the righthand column which appear next to odd numbers in the left hand column, you recover the original (unknown) product. (As you indicate, 54 * 19 = 608 + 304 + 76 + 38. The point is that 54 * 19 = 27 * 38 = 13 * 76 + 38 = 6 * 152 + 76 + 38 = 3 * 304 + 76 + 38 = = 1 * 608 + 304 + 76 + 38. )
In my opinion, bringing binary numbers into the explanation just makes it more confusing.
See <Http://www.math.Hawaii.Edu/~lee/elementary/Lazy2.pdf> ("Bride of the Lazy Man").
 Trying to understand learning by studying schooling is rather like trying to understand sexuality by studying bordellos.  Mary Catherine Bateson, Peripheral Visions lady@Hawaii.Edu



