Ancient Egyptians liked to represent fractions as sums of reciprocals, though they sometimes used fractions like 2/3 and 3/4.

- Egyptian fraction
- Rhind Mathematical Papyrus ~ 1550 BCE
- Greedy algorithm for Egyptian fractions
- Rhind Mathematical Papyrus 2/n table
- Egyptian Fraction -- from Wolfram MathWorld
- Egyptian Fractions
- Egyptian Fractions - Algorithms for Egyptian Fractions
- Egyptian Fractions

That 2/n table:

- 2/3 = 1/2 + 1/6
- 2/5 = 1/3 + 1/15
- 2/7 = 1/4 + 1/28
- 2/9 = 1/6 + 1/18
- 2/11 = 1/6 + 1/66
- 2/13 = 1/8 + 1/52 + 1/104
- 2/15 = 1/10 + 1/30
- 2/17 = 1/12 + 1/51 + 1/68
- 2/19 = 1/12 + 1/76 + 1/114
- Etc. to 2/101

The Rhind papyrus's multiples of 1/10:

- 1/10 = 1/10
- 2/10 = 1/5
- 3/10 = 1/5 + 1/10
- 4/10 = 1/3 - 1/15
- 5/10 = 1/2
- 6/10 = 1/2 + 1/10
- 7/10 = 2/3 + 1/30
- 8/10 = 2/3 + 1/10 + 1/30
- 9/10 = 2/3 + 1/5 + 1/30

From some of these examples, it is possible to guess at what algorithms were used.

Like:

2/n = 1/m + (2m-n)/(m*n)

n/(p*q) = 1/(p*r) + 1/(q*r) where r = (p+q)/n