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 results in an equivalent fraction with the smallest possible whole numbers.

2. How Does the Calculator Work?

The calculator uses the following formula:

Where:

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

Explanation: The calculator first finds the GCD of the numerator and denominator using the Euclidean algorithm, then divides both numbers by this GCD to get the simplified fraction.

3. Importance of Simplifying Fractions

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

4. Using the Calculator

Tips: Enter positive integers for both numerator and denominator. The calculator will find the GCD and display the simplified fraction. For mixed numbers, simplify the fractional part separately.

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, indicating it cannot be simplified further.

Q2: Can this calculator handle improper fractions?
A: Yes, it works with both proper and improper fractions. For mixed numbers, convert to improper fraction first.

Q3: What's the maximum number this calculator can handle?
A: It depends on your server's PHP configuration, but typically handles numbers up to 2 billion.

Q4: How does the Euclidean algorithm work?
A: It repeatedly replaces the larger number with its remainder when divided by the smaller number until one number becomes zero.

Q5: Can I simplify negative fractions?
A: This calculator only handles positive integers. For negative fractions, simplify the absolute values and keep the negative sign.