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What are unit fractions and how are they tied to ancient Egypt?

Aunit fraction is one that has a numerator of 1, such as ½, 1/4, and 1/43545. One of the earliest discussions of unit fractions—a table of representations of 1/n—was found on the famous Rhind papyrus (also called the Rhind Mathematical Papyrus), dated to around 1650 B.C.E. This record—a table copied by the Egyptians from another papyrus dated 200 years earlier—represented a sum of distinct unit fractions for odd “n” numbers between 5 and 101. To write a certain fraction, they would add combinations of 1/n. For example, instead of writing 2/5, they wrote 1/3 + 1/15; for 2/29, they wrote 1/24 + 1/58 + 1/174 + 1/232.

Because of the Rhind papyrus discovery, the sums of unit fractions are now called Egyptian fractions. No one truly knows why the Egyptians chose this method for representing fractions, but some historians believe it was a “wrong turn” in Egyptian mathematical history. Whatever the reason, the Egyptians (apparently successfully) used this system for 2,000 years. (For more information about the Rhind papyrus, see “History of Mathematics.”)

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