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Cliff Rohrabacher
03-12-2007, 5:22 PM
Shamelessly stolen from:
>http://mathforum.org/dr.math/faq/faq.peasant.html#whatis<

We learned to multiply like so:
57
86
----
4902



Write each number at the head of a column.
Double the number in the first column, and halve the number in the second column.
If the number in the second column is odd, divide it by two and drop the remainder.
If the number in the second column is even, cross out that entire row.
Keep doubling, halving, and crossing out until the number in the second column is 1.
Add up the remaining numbers in the first column. The total is the product of your original numbers.

Let's multiply 57 by 86 as an example:

Write each number at the head of a column.
57 86


Double the number in the first column, and halve the number in the second column.
57-------- 86
114 ------ 43


If the number in the second column is even, cross out that entire row.
57------- 86
114------ 43


Keep doubling, halving, and crossing out until the number in the second column is 1.
57 ------ 86
114 ------ 43
228 ------ 21
456------ 10
912------- 5
1824 ------ 2
3648------ 1


Add up the remaining numbers in the first column.
57-------- 86
114 -------43
228 ------ 21
456------ 10
912-------- 5
1824------- 2
3648 ------1
Result: 4902


Real Russian peasants may have tracked their doublings with bowls of pebbles, instead of columns of numbers. (They probably weren't interested in problems as large as our example, though; four thousand pebbles would be hard to work with!) Russian peasants weren't the only ones to use this method of multiplication. The ancient Egyptians invented a similar process thousands of years earlier, and computers are still using related methods today.

Aaron Koehl
03-13-2007, 12:06 AM
Interestingly enough, that is essentially binary multiplication... shift, add, shift, add, shift..

Dennis Peacock
03-13-2007, 10:34 AM
That's about computer math....all over again. :D