1. What is Fraction Simplification?

Fraction simplification (reducing to lowest terms) means dividing both numerator and denominator by their greatest common divisor (GCD) to obtain an equivalent fraction with the smallest possible whole numbers.

2. How Does the Calculator Work?

The calculator uses the following process:

Where:

• GCD — Greatest Common Divisor of numerator and denominator
• Numerator — Top number of the fraction
• Denominator — Bottom number of the fraction

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

3. Importance of Simplified Fractions

Details: Simplified fractions are easier to work with in calculations, comparisons, and provide the most reduced form which is often required in mathematical solutions.

4. Using the Calculator

Tips: Enter positive integers for both numerator and denominator. The calculator will automatically find and apply the GCD.

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 note that it was divided by GCD: 1.

Q2: Can I simplify 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 simplifying.

Q4: How is the GCD calculated?
A: Using the Euclidean algorithm, which efficiently finds the greatest common divisor.

Q5: Can this handle very large numbers?
A: Yes, within PHP's integer limits (typically up to 2 billion).