1. What is Fraction Reduction?

Fraction reduction, also known as simplifying fractions, is the process of expressing a fraction in its simplest form where the numerator and denominator have no common divisors other than 1.

2. How Does the Calculator Work?

The calculator uses the greatest common divisor (GCD) method:

Where:

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

Explanation: The calculator finds the largest number that divides both numerator and denominator exactly, then divides both by this number.

3. Importance of Reducing Fractions

Details: Simplified fractions are easier to work with in calculations, comparisons, and provide the most basic form of representing a ratio or portion.

4. Using the Calculator

Tips: Enter positive integers for both numerator and denominator. The calculator will display the reduced form and the GCD used.

5. Frequently Asked Questions (FAQ)

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

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

Q3: What about mixed numbers?
A: Convert mixed numbers to improper fractions first before using this calculator.

Q4: How is the GCD calculated?
A: Using the Euclidean algorithm, an efficient method for finding GCD.

Q5: What's the largest number this can handle?
A: The calculator can handle very large numbers, limited only by PHP's integer size.