1. What is Fraction Simplification?

Fraction simplification is the process of reducing a fraction to its lowest terms by dividing both the numerator and denominator by their greatest common divisor (GCD). The simplified fraction has the same value as the original but with smaller numbers.

2. How Does the Calculator Work?

The calculator uses the following formula:

Where:

• \( \text{num} \) — The numerator of the fraction
• \( \text{den} \) — The denominator of the fraction
• \( \text{gcd(num, den)} \) — Greatest common divisor of numerator and denominator

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

3. Importance of Simplified 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 easier to interpret.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What if my fraction is already in simplest form?
A: The calculator will return the same fraction with a GCD of 1.

Q2: Can I simplify improper fractions?
A: Yes, the calculator works with both proper and improper fractions.

Q3: What's the largest fraction this can simplify?
A: The calculator can handle very large numbers, limited only by PHP's integer size.

Q4: Does this work with negative numbers?
A: This version only accepts positive integers. Negative numbers would require additional handling.

Q5: How is the GCD calculated?
A: Using the Euclidean algorithm, which efficiently finds the greatest common divisor.