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, 6th Edition. Pacific Grove: Thompson Learning, Inc.
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