Egyptian Fractions Calculator

Your details

The top number of your fraction. Must be a positive integer.
The bottom number of your fraction. Must be a positive integer greater than 0.
Greedy takes the largest possible unit fraction at each step. Splitting repeatedly peels off 1/denominator. Best tries all methods and returns the shortest result.
Egyptian fraction expansion
1/2 + 1/4

The fraction written as a sum of distinct unit fractions

Number of terms2
Largest denominator4
Method usedGreedy (Fibonacci-Sylvester)
Reduced input3/4
Number of terms2
Largest denominator4

3/4 = 1/2 + 1/4

  • Your fraction 3/4 decomposes into 2 distinct unit fractions.
  • The largest denominator in the expansion is 4, which is quite compact.
  • A two-term expansion is among the most compact possible; the Rhind Papyrus used two-term forms frequently because they were easiest to work with in practice.

Next stepExperiment with the "Best (fewest terms)" algorithm to compare approaches, or try fractions like 2/7 and 3/11 that appear in the historical Rhind Papyrus tables.

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