## Egyptian Multiplication

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.

```     13	  7