Black History Month Activity

Egyptian Multiplication

The ancient Egyptians probably migrated to Egypt from the Sahara region of Africa. The Egyptians were one of the great ancient civilizations.

They used a hieroglyphic system for numbers in which each number was a picture of an object.

Suppose an Egyptian needed to multiply 12 by 3.

In Egyptian numerals, the number 12 is written

so three lots of 12 should be

If we collect all the tens together and tidy up the layout a little, we get the answer

This is exactly right - it's the number 36 in ancient Egyptian numerals.

This shows how multiplication can be thought of as repeated addition.

Can you imagine doing this with large numbers without losing count anywhere? What a nightmare!

Fortunately the ancient Egyptians were very clever. They used a technique called duplation that forms the basis of arithmetic on many computer systems.

"Duplation" means "doubling", and this is what we do; we keep doubling one of the numbers while halving the other (ignore any remainders) - we stop when the second number is halved all the way down to 1.

Let's try multiplying out 48 by 29 using duplation.

Doubling	Halving	Odd?
48	29	yes
96	14
192	7	yes
384	3	yes
768	1	yes

Now add together the numbers in the doubling column that correspond to odd values in the halving column. This gives the correct answer,

48 + 192 + 384 + 768 = 1392

Now its your turn

59 × 26 =	64 × 37 =	426 × 84 =
Check the answers