Egyptian Fraction Calculator

Math

The Egyptian Fraction Calculator expresses a proper fraction as a sum of distinct unit fractions using the greedy (Fibonacci–Sylvester) algorithm. Enter a numerator and denominator.

Formula

Greedy algorithm: repeatedly subtract the largest unit fraction 1/⌈den/num⌉
  • Every positive proper fraction can be written as a sum of distinct unit fractions.
  • The greedy method always terminates.

4/13

Inputs
  • Numerator: 4
  • Denominator: 13

4/13 = 1/4 + 1/18 + 1/468.

Frequently asked questions

What is an Egyptian fraction?
A sum of distinct unit fractions (each with numerator 1), as used in ancient Egyptian mathematics.