Date: Mar 3, 1998 9:26 PM
Author: Lee Lady
Subject: Re: Russian Peasant Multiplication: Explained!

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 non-proportional 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 left-hand 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 left-hand column is

odd, this is not quite correct. The discrepancy is in fact the number in

the right-hand column. (For instance, 27 * 38 = 13 * 76 + 38.)

Now if you take the final entry in the right-hand column and add to it

all the discrepancies, i.e. all the other entries in the right-hand

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