This lesson describes a method of multiplication used by the ancient Egyptians. The method of multiplication is such that it is only necessary to add and to multiply by twos - memorization of multiplication tables is unnecessary.
To introduce students to the use of characters for numbers (hieroglyphics).
To show students how numbers can be written additively.
To expose students to a multiplication method from a non-European culture.
hieroglyphics
additive numbers
multiplication
multiplication tables
notation
Egyptian Multiplication could be used in a basic skills mathematics, prealgebra or algebra course to reinforce or introduce the concept of multiplication of whole numbers.
The ancient Egyptians probably migrated to Egypt from the once fertile Sahara region of Africa. These early inhabitants of Africa were referred to as "Ethiopians", and the customs of the Egyptians were quite similar to those of the Ethiopians, or Africans. Egyptian civilization, one of the great ancient civilizations, included methods of flood control, irrigation and marsh drainage as well as a centralized government, a calendar, and a standard system of weights and measures. Egypt’s best known mathematical and cultural legacy is its pyramids.
Egyptians used a hieroglyphic system for numbers in which each character was a picture of an object which in turn represented a number. The Egyptian number system used these symbols:
(hieroglyphics available in Word document)
Numbers are written by using the symbols additively, starting with the smallest numbers on the left and moving toward the largest on the right.
For example:
13012 = 2 + 1(10) + 3(103) + 1(104)
The Egyptians had a way of doing multiplication where they only had to add and to multiply by twos. They never had to memorize multiplication tables! A variation of their method is still used today in rural communities of Ethiopia, Russia, the Arab world, and the Near East. For example:
Multiply 37 by 14
Choose 37 as the multiplicand, and then multiply 37 by 2, then by 2 again (or 37 by 4), then by 2 again (or 37 by 8). Stop now because the next multiplier (by 2 again or 16) is greater than the number being multiplied, 14. The numbers in the left column that add up to 14 are marked with asterisks, and their corresponding sums in the right column are added. This number is the answer to the multiply problem (37 times 14 equals 518).
1. Multiply 57 by 13 using Egyptian multiplication.
2. Show your work in both Modern and Egyptian notation.
3. Check your answer using American multiplication.
Gullberg, Jan. (1997). Mathematics: From the Birth of Numbers. New York: W.W. Norton & Company.
Joseph, George Gheverghese. (1991). The Crest of the Peacock: Non-European Roots of Mathematics. London: Penguin Books.
Nelson, D., Joseph, G. and Williams, J. (1993). Multicultural Mathematics: Teaching Mathematics from a Global Perspective. New York: Oxford University Press.