Math

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Egyptian Fraction Calculator.

Decompose a positive proper fraction into a sum of distinct unit fractions using the greedy algorithm.

On-device calculationNo signup
01

Set your values

Results update as you type.

terms: 1/4 + 1/18 + 1/468

terms

1/4 + 1/18 + 1/468
termCount: 3

termCount

3.000000

Results update automatically as you type.

Use Cases

Educational tool for math students

Helps students understand the concept of unit fractions and how to decompose fractions, a key topic in number theory and history of mathematics.

Example: Decompose 5/6 into 1/2 + 1/3.

Historical math exploration

Allows enthusiasts to explore how ancient Egyptians represented fractions, providing insight into their numeral system.

Example: See how 7/10 becomes 1/2 + 1/5.

Frequently Asked Questions

What is an Egyptian fraction?
An Egyptian fraction is a sum of distinct unit fractions, where each unit fraction has a numerator of 1 and a different denominator. For example, 3/4 can be written as 1/2 + 1/4. This calculator decomposes a given proper fraction into such a sum.
How does the Egyptian Fraction Calculator work?
You enter the numerator and denominator of a proper fraction (where numerator is less than denominator). The calculator uses a greedy algorithm to find a sequence of distinct unit fractions that sum to the original fraction, displaying the decomposition step by step.
Can I use this calculator for improper fractions?
No, this calculator is designed for proper fractions only, where the numerator is less than the denominator. If you enter an improper fraction, the result may not be a valid Egyptian fraction representation.

Tips & Common Mistakes

Tips

  • Ensure the numerator is less than the denominator for a proper fraction.
  • Use positive integers for both numerator and denominator.
  • The calculator uses a greedy algorithm, which may not always produce the shortest representation, but it always works.
  • Check your inputs for common factors; the calculator will handle simplification automatically.

Common Mistakes to Avoid

  • Entering a numerator greater than the denominator, which results in an improper fraction.
  • Using zero or negative numbers, which are not valid for this calculator.
  • Expecting the calculator to show all possible decompositions; it shows one valid representation.

Last updated: August 13, 2026