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 formula:

Where:

• \( a \) — Numerator (unitless)
• \( b \) — Denominator (unitless)
• \( g \) — Greatest common divisor of a and b (unitless)

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

5. Frequently Asked Questions (FAQ)

Q1: What if my fraction is already in lowest terms?
A: The calculator will return the same fraction with a GCD of 1, confirming it's already simplified.

Q2: Can I use this for negative numbers?
A: This calculator is designed for positive integers only. For negative fractions, you would simplify the absolute values and apply the sign to the numerator.

Q3: What's the largest number this 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).

Q4: How is the GCD calculated?
A: The calculator uses the Euclidean algorithm, an efficient method for computing the GCD of two numbers.

Q5: Can this handle improper fractions?
A: Yes, the calculator works with both proper and improper fractions.