Some Egyptian mathematics…

The Egyptians did their very best to avoid messy computations with fractions by expressing all fractions, other than 2/3, as the sum of unit factions. They created tables that that made these representations easier. So, 2/7 can be expressed as 1/4+1/28. It can be a challenge to represent fractions as unit fractions as the Egyptians once did:

Represent 2/99 as a unit fraction in 2 different ways:

2/99=1/66+1/198

2/99=1/11+1/9

The Egyptians also had a very interesting way of multiplying large numbers. Say we want to multiply 2 numbers, 24 and 55. The Egyptians took one numbers, and halved it until the number 1 was reached. At the same time, they doubled the other number as many times as it took to obtain 1 from halving the first number. Then, the numbers of the doubling column that correspond to the odd numbers of the halving column are added together to reach the final answer.

24	55
12	110
6	220
3	440
1	880

So adding the numbers that were doubled correspond to the odd numbers of the halved column, we see that 440+880=1320. If we check with our modern, handy calculator, we see that indeed, 24*55=1320.

Using this method of multiplication, have the students multiply larger numbers. Maybe this will give everyone a greater appreciation for the technology around us!

Eves, H. (1990). An introduction to the history of mathematics, 6^th Edition. Pacific Grove: Thompson Learning, Inc.

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