Egyptian Fractions Calculator

Express a fraction as a sum of distinct unit fractions.

Unit-fraction sum 1/2 + 1/3

Number of terms 2

Formula: Greedy algorithm: subtract the largest possible 1/n each step

Step-by-step with your numbers:

1. Values used:

2. Numerator = 5

3. Denominator = 6

5. Unit-fraction sum = 1/2 + 1/3

6. Number of terms = 2

Did we solve your problem today?

Ancient Egyptians wrote every fraction as a sum of distinct unit fractions (1/n).

The math behind it

Fibonacci's greedy algorithm repeatedly subtracts the largest unit fraction not exceeding the remaining value, guaranteeing a finite expansion.

5/6 = 1/2 + 1/3.

Is the expansion unique?

No — a fraction can have several Egyptian representations; the greedy method gives one of them.