1. What is Fraction Simplification?

Fraction simplification is the process of reducing a fraction to its lowest terms by dividing both the numerator and denominator by their greatest common divisor (GCD). This creates an equivalent fraction that is easier to work with and understand.

2. How Does the Calculator Work?

The calculator uses the following mathematical process:

Where:

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

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

3. Importance of Simplified Fractions

Details: Simplified fractions are easier to compare, add, subtract, multiply, and divide. They provide the most reduced form of a fraction which is essential for mathematical operations and real-world applications.

4. Using the Calculator

Tips: Enter positive integers for both numerator and denominator. The calculator will automatically compute and display the simplified form.

5. Frequently Asked Questions (FAQ)

Q1: What if my fraction is already in simplest form?
A: The calculator will return the same fraction, indicating it's already simplified.

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 does this compare to Desmos's fraction tool?
A: This provides similar functionality to Desmos's fraction simplification feature in a standalone calculator.

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