Egypt's Unit Fractions

The Egyptians had a curious limit: they wrote almost every fraction with a numerator of 1 (called unit fractions). To express 2/5, they wrote 1/3 + 1/15. To express 2/7, they wrote 1/4 + 1/28. The Rhind Papyrus (1650 BC) holds a table turning every fraction of the form 2/n into such sums.

This looks clumsy, but it had a practical edge for sharing goods: "give each person 1/3 of a loaf plus 1/15 of a loaf" is easier to cut and hand out than "give each person 2/5 of a loaf." The notation matched the physical act of dividing.

The idea never fully went away — finding the shortest way to write a fraction as a sum of distinct unit fractions is still an open puzzle that mathematicians study today.