➗ Java Fraction Arithmetic Library

An Object-Oriented Java library designed to represent and perform arithmetic operations on fractions. This project ensures data integrity through strict validation and automatic mathematical simplification.

✨ Key Features

• Automatic Simplification: Every fraction is automatically reduced to its simplest form using the Greatest Common Divisor (GCD) algorithm during construction.
• Robust Validation: Enforces rules to prevent division by zero and handles negative denominators by terminating the program with clear error messages.
• Constructor Chaining: Demonstrates advanced OOP patterns using this(1, 1) to link constructors for consistent initialization.
• Arithmetic Suite: Full support for:
  • Add(Fraction f2)
  • Subtract(Fraction f2)
  • Multiply(Fraction f2)
  • Divide(Fraction f2)

🧮 Mathematical Logic

1. GCD & Reduction

The reduce() method is marked as private final to protect the internal logic. It utilizes a custom GCD function: $$gcd(a, b) = \max {g \in \mathbb{Z} : g|a \text{ and } g|b}$$

2. Copy Constructor

Implemented to allow safe duplication of objects without affecting the original instance, a core concept in effective memory management and object integrity.

🚀 Example Usage

Enter first fraction's numerator: 4
Enter first fraction's denominator: 16
Enter second fraction's numerator: 6
Enter second fraction's denominator: 10

x + y = 17/20
x - y = -7/20
x * y = 3/20
x / y = 5/12