Archive for June 9th, 2009

Ethiopian Multiplication

June 9, 2009

plastic_numbersOne of our recent (oh my goodness has it really been seven years???) grads just sent me this Youtube video of Ethiopian Multiplication, with a note that this reminded her of History of Mathematics.  Which, of course, made me totally happy.

This method of multiplication is also called Egyptian Multiplication (because it was done in Egypt) and Russian Peasant Multiplication (although the Peasant part might be intended as a bit of a pejorative).

Here’s the basic idea:  Suppose you want to multiply two numbers like 14 and 12.  You could use your fingers, of course, but here’s another way:

Start with the two numbers on top.  Halve one, ignoring any remainders or fractions, and double the other, stopping when you get to 1.

14 & 12

7 & 24

3 & 48  [See how I ignored the fact that halving 7 leaves 1 left over?]

1 & 96  <— Stop here.

Now look at the numbers on the right.  Some are across from an even number: in this case, 12 is across from the original 14.  Ignore those, and add the rest.  So we’ll add 24, 48, and 96, which were across from odd numbers, and get 168.  And that’s the product!  Isn’t that cool?

(I think it would be fantastic to write a book called 25 ways to multiply.  I only have about 13 at the moment, though.)

Here’s the video!

Number photo from gokuro.