Egyptian Fractions Calculator
Convert any fraction into a sum of distinct unit fractions (Egyptian fractions) using the greedy algorithm. Learn how the ancient Egyptians represented fractions.
Step 1: Enter Fraction
About Egyptian fractions
An Egyptian fraction is a sum of distinct unit fractions (1/2, 1/3, 1/4, …). Every positive rational number can be represented this way. The greedy algorithm (Fibonacci’s method) always finds a representation, though not always the shortest.
Step 2: Representation Options
Greedy algorithm
For a fraction p/q, find the smallest n such that 1/n ≤ p/q. Then subtract and repeat. This calculator uses the exact integer method to avoid floating errors.
Egyptian Fraction Result
Summary
Step‑by‑Step
Other representations
Egyptian fraction representation
½ + ¼
for 3/4
Number of terms
2
Largest denominator
4
Decimal value
0.75
Sum of unit fractions
3/4
Unit fraction blocks (approx. size)
Greedy algorithm steps
- Step 1: 3/4 → take 1/2, remainder 1/4
- Step 2: 1/4 → take 1/4, remainder 0
Alternative representations (short / different)
| Method | Representation | Terms |
|---|---|---|
| Greedy (current) | 1/2 + 1/4 | 2 |
| Optimal (shortest known) | 1/2 + 1/4 | 2 |
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