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© Copyright 1999, Jim Loy
Ancient Egyptians sometimes multiplied in the following way (using a kind of base-2 arithmetic). Apparently, they also used other methods. We will use 7x13 as an example. We make two columns. We start with 1 and 7 (one of the numbers we want to multiply). Then we double the number in each column, over and over until we get to a number just below the other number (13 in this case) in the left-hand column:
1 7 2 14 4 28 8 56 --------
We have powers of two in the left column, and we have 7 times the powers of two in the right column. We can make 13 out of the left column, by 8+4+1. That is where the base 2 arithmetic comes in. We mark those numbers (8, 4, 1). And we add up the numbers in the second column, skipping the ones that are not next to a marked power of two:
/1 7
2 14
/4 28
/8 56
---------
91
That is the right answer. There is a very similar method called Russian or Ethiopian Multiplication. Apparently, powers of ten were sometimes used as well:
/10 70
/1 7
/2 14
---------
91
This may be viewed as a short cut. Instead of 13 being 8+4+1, it becomes 10+2+1. For larger numbers, this short cut shortens the process considerably.
Also see Egyptian Fractions.
Addendum:
Russian (Ethiopian) multiplication works like this (calculating 13x7):
13 7
6 (14)
3 28
1 56
-------
91
Instead of doubling in the left column, we divide by two (dropping fractions). And we cross out (parentheses in my example) any number in the right column that is next to an even number in the left column. This is very similar to Egyptian multiplication. Notice that the right column here is the same as the right column at the top of this article.