Egyptian Fractions Calculator

Enter a proper fraction with numerator and denominator, then click Calculate Egyptian Fraction. The result panel shows the unit-fraction expansion and each intermediate greedy step from the starting fraction to zero remainder.

This implementation keeps the numerator range between 1 and 5 so the decomposition remains readable.

Egyptian fraction form: - a/b = 1/n1 + 1/n2 + ... + 1/nk, with all denominators distinct.

Greedy decomposition rule: - For current n/d, pick u = ceil(d/n), subtract 1/u, simplify the remainder, and repeat.

The process always terminates for proper fractions and returns one valid expansion.

Egyptian fractions are a historical fraction-writing system where values are expressed as sums of non-repeating unit fractions. Although modern notation is shorter, Egyptian decompositions are still valuable for learning fraction structure and algorithmic reasoning.

Because multiple decompositions may exist for the same fraction, this calculator uses one consistent strategy (greedy splitting) so results are predictable and easy to verify.