Unlock the secrets of ancient Egyptian mathematics with our free online Egyptian Fractions Calculator. Easily convert any proper fraction (e.g., 3/7) into its equivalent sum of distinct unit fractions (e.g., 1/3 + 1/11 + 1/231). Perfect for students, educators, and anyone exploring number theory and historical math concepts.
Formula:
An Egyptian fraction is a sum of distinct unit fractions, where a unit fraction is a reciprocal of a positive integer (e.g., 1/2, 1/5). For a proper fraction n/d (where n is the numerator and d is the denominator), the calculator applies the greedy algorithm (also known as the Fibonacci-Sylvester method):
- Find the smallest integer
xsuch that1/x ≤ n/d. This valuexis calculated asceil(d/n). - Add
1/xto the list of unit fractions. - Calculate the remaining fraction by subtracting
1/xfromn/d. - Repeat the process with the new remaining fraction until the numerator becomes 0 or 1.
Example: To decompose 3/7, the result would be 1/3 + 1/11 + 1/231.