Fraction Decomposition Calculator
Break a fraction into a mixed number plus unit fractions
Fraction Decomposition Calculator
Table of Contents
How to Use
- Enter a positive numerator and denominator
- Click Decompose fraction
- Review the mixed number and remaining fraction
- Study the unit fractions and steps
What is an Egyptian fraction?
An Egyptian fraction represents a positive rational number as a sum of distinct unit fractions (fractions with numerator 1). For example 5/6 = 1/2 + 1/3.
Why it matters
Egyptian decompositions help illustrate how rational numbers can be built from simple reciprocals and make for engaging number theory exercises.
Greedy method overview
The greedy algorithm repeatedly subtracts the largest possible unit fraction. Take the ceiling of denominator ÷ numerator to get the next term, subtract it, and repeat until no remainder remains.
- Identify the whole-number part of the fraction
- Use the remainder for Egyptian decomposition
- Stop once the remainder becomes zero