1. What is Fraction Simplification?

Fraction simplification is the process of reducing a fraction to its simplest form where the numerator and denominator have no common divisors other than 1. This is done by dividing both numerator and denominator by their greatest common divisor (GCD).

2. How Does the Calculator Work?

The calculator uses the following mathematical process:

Where:

• \( a \) — Numerator (integer)
• \( b \) — Denominator (integer)
• \( \gcd(a,b) \) — Greatest common divisor of a and b

Explanation: The calculator first finds the GCD of the numerator and denominator using the Euclidean algorithm, then divides both numbers by this GCD to get the simplified fraction.

3. Importance of Simplifying Fractions

Details: Simplified fractions are easier to work with in calculations and comparisons. They represent the same value in the most reduced form, making mathematical operations more efficient and results more interpretable.

4. Using the Calculator

Tips: Enter positive integers for both numerator and denominator. The calculator will display the original fraction, the GCD, and the simplified fraction.

5. Frequently Asked Questions (FAQ)

Q1: What if I enter a numerator larger than the denominator?
A: The calculator works the same way for proper and improper fractions. It will simplify any valid fraction.

Q2: What happens if I enter two prime numbers?
A: If the numerator and denominator are co-prime (GCD = 1), the fraction is already in simplest form and will be returned unchanged.

Q3: Can this calculator handle negative numbers?
A: This version only accepts positive integers. Negative numbers would require additional sign handling.

Q4: What's the largest number this can handle?
A: The calculator is limited by PHP's integer size (typically ±2 billion on 32-bit systems). For very large numbers, specialized algorithms may be needed.

Q5: How is the GCD calculated?
A: The calculator uses the Euclidean algorithm, an efficient method for computing the GCD of two numbers.