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 cannot be simplified further.

2. How Does the Calculator Work?

The calculator uses the following mathematical principle:

Where:

• \( a \) — Numerator (unitless)
• \( b \) — Denominator (unitless)
• \( g \) — Greatest Common Divisor of a and b (unitless)

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

3. Importance of Lowest Terms

Details: Fractions in lowest terms are easier to work with in calculations and comparisons. They represent the simplest form of the ratio between two numbers.

4. Using the Calculator

Tips: Enter positive integers for both numerator and denominator. The calculator will return the GCD and the reduced fraction in lowest terms.

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

Q3: Can I use this for negative numbers?
A: This calculator is designed for positive integers only. For negative numbers, you would reduce the absolute values and then apply the sign to the numerator.

Q4: What's the largest number this calculator can handle?
A: The calculator can handle numbers up to PHP's integer limit (typically 2^31-1 or 2^63-1 depending on your system).

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