Last updated: July 31, 2026
Egyptian Fractions Calculator
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Formula
numerator/denominator = Σ(1/di) using greedy Egyptian-fraction decomposition
Where:
- numerator=numerator
- denominator=denominator
Worked Examples
4/13 decomposition
Classic greedy decomposition example.
- 1Pick 1/4 then reduce remainder
- 2Continue greedily until remainder is zero
2/3 decomposition
Simple two-term decomposition.
- 1Pick 1/2
- 2Remainder is 1/6
3/7 decomposition
Another proper fraction.
- 1Pick 1/3 then reduce
- 2Finish with 1/11 and 1/231
Introduction
Decompose a proper fraction into distinct unit fractions using the Fibonacci-Sylvester greedy algorithm.
Formula and Method
Egyptian Fractions Calculator uses: numerator/denominator = Σ(1/di) using greedy Egyptian-fraction decomposition
Enter all required inputs
Apply the underlying math formula(s)
Compute supporting terms where needed
Round numeric outputs for stable display
Input Fields
Provide values for: numerator, denominator.
- 1
numerator: numerator
- 2
denominator: denominator
Output Fields
The calculator returns: unitFractions, termCount.
- 1
unitFractions: Egyptian fraction expansion as a sum of unit fractions
- 2
termCount: Number of unit-fraction terms in the expansion
Validation Rules
Input validation is applied before calculation to prevent invalid math states.
numerator and denominator must be positive integers.
numerator must be smaller than denominator (proper fraction).
Algorithm is capped at 20 terms for safety.
If decomposition fails, the calculator returns an error state.
How to Use This Calculator
Fill in the inputs, run the calculator, and review primary output first.
Enter the required values
Click calculate
Check the primary output
Use example scenarios for verification
Practical Uses
This calculator supports learning, quick checks, and day-to-day technical problem solving.
Homework and exam preparation
Engineering and science sanity checks
Classroom demonstrations
Fast recalculation with different inputs
FAQs
What does the Egyptian Fractions Calculator compute?
Decompose a proper fraction into distinct unit fractions using the Fibonacci-Sylvester greedy algorithm.
Which inputs are required?
Required inputs: numerator, denominator.
How should I format numbers?
Use finite numeric values; decimals and negative numbers are allowed unless restricted by validation rules.
How are results rounded?
Numeric outputs are rounded to about 6 decimal places for readability.
Why might I see an error?
numerator and denominator must be positive integers.
Can I use this for learning and verification?
Yes. Use the examples and formula section to verify manual calculations quickly.