How to Add and Subtract Like an Egyptian

What do drawings of ropes, fingers, and flowers have to do with math? Keep on reading to learn how the ancient Egyptians used these and many other hieroglyphs to count numbers!

Jason Marshall, PhD,
February 26, 2016
Episode #138

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Egyptian Numbers

About 5,000 years ago the ancient Egyptians developed a hieroglyphic system that was definitely an improvement. As we’ll soon see and appreciate, the key to this system is the idea that it’s much more efficient to use many symbols to represent numbers rather than just the single symbol used by the tally-bone carvers. The first five symbols in the ancient Egyptian numeral system are:

Notice that the symbol for the number 1 is basically a notch—exactly like the one our tally-bone carving friends used. And, not coincidentally, it looks a lot like our numeral “1”. But that’s where the similarity to the tally-bone system ends since the Egyptians also had symbols for the numbers 10 (shaped like a yoke used to plow fields), 100 (a twisted length of rope), 1000 (a rather cheerful looking flower), 10,000 (a finger), 100,000 (a frog), and 1,000,000 (a happy human with arms raised to the sky). But what about the numbers 2, 3, and everything else that doesn’t have a unique hieroglyph?

Egyptian Arithmetic

All numbers that don’t have their own symbols are written by adding two or more symbols together—basic arithmetic! For example, the ancient Egyptians would write the number 2 by writing the symbol for the number 1 two times. But, you might be thinking, that’s exactly like the tally-bone system! How is this more efficient? Well, the efficiency comes from using those extra symbols we’ve seen for higher powers of 10. So although the ancient Egyptians did have to write an extra hieroglyph for each number between 2 and 9, when they got to 10 they returned to writing only a single symbol. Then, to represent a number like 36, all you have to do is write down 3 hieroglyphs that each represent 10 next to 6 hieroglyphs that each represent 1, which represents a total of (3 x 10) + (6 x 1) = 36.



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