1. What is Fraction Reduction?

Fraction reduction is the process of simplifying a fraction to its lowest terms by dividing both the numerator and denominator by their greatest common divisor (GCD). This results in an equivalent fraction that is easier to work with and understand.

2. How Does the Calculator Work?

The calculator uses the following method:

Where:

• \( Num \) — The numerator of the fraction
• \( Den \) — The denominator of the fraction
• \( GCD \) — Greatest common divisor of numerator and denominator

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

3. Importance of Fraction Reduction

Details: Reduced fractions are essential in mathematics for simplifying calculations, comparing fractions, and presenting final answers in their simplest form. They're used in algebra, calculus, and everyday calculations.

4. Using the Calculator

Tips: Enter positive integers for both numerator and denominator. The calculator will find the GCD and reduce the fraction to its simplest form.

5. Frequently Asked Questions (FAQ)

Q1: What if I enter a numerator larger than the denominator?
A: The calculator works the same way - it will reduce the improper fraction to its simplest form.

Q2: Can this calculator handle negative fractions?
A: This version only accepts positive integers. The negative sign would typically be applied to the whole fraction.

Q3: What's the maximum number this calculator can handle?
A: It depends on your server's PHP configuration, but typically up to 2,147,483,647 for 32-bit systems.

Q4: How is the GCD calculated?
A: Using the Euclidean algorithm, which efficiently finds the GCD through repeated division.

Q5: What if I enter two prime numbers?
A: If the numerator and denominator are co-prime (GCD=1), the fraction is already in its simplest form.