1. What is Fraction Simplification?

Fraction simplification is the process of reducing a fraction to its simplest form by dividing both the numerator and denominator by their greatest common divisor (GCD). This creates an equivalent fraction with the smallest possible whole numbers.

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 finds the GCD of the numerator and denominator, then divides both by this value to produce the simplified fraction.

3. Importance of Simplified Fractions

Details: Simplified fractions are easier to work with in calculations and comparisons. They represent the same value in the most reduced form, making mathematical operations more efficient and results more understandable.

4. Using the Calculator

Tips: Enter any positive whole numbers for numerator and denominator. The calculator will find the GCD and display the simplified fraction.

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 GCD of 1.

Q2: Can I simplify fractions with decimals?
A: This calculator works with whole numbers only. For decimal fractions, multiply numerator and denominator by 10^n to eliminate decimals first.

Q3: What's the maximum 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).

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

Q5: Can this calculator handle negative numbers?
A: This version only accepts positive integers. Negative fractions would require handling signs separately.