1. What is a Simplified Fraction?

A simplified fraction (or fraction in simplest form) is a fraction where the numerator and denominator have no common divisors other than 1. This is achieved by dividing both numerator and denominator by their greatest common divisor (GCD).

2. How Does the Calculator Work?

The calculator uses the following process:

Where:

• GCD is calculated using the Euclidean algorithm
• Numerator and denominator must be positive integers
• The fraction is reduced to its simplest form

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

3. Importance of Simplifying 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.

4. Using the Calculator

Tips: Enter positive integers for both numerator and denominator. The calculator will display the simplified fraction and the GCD used to simplify it.

5. Frequently Asked Questions (FAQ)

Q1: What if I enter a numerator larger than the denominator?
A: The calculator works the same way. It will simplify the improper fraction, which you could then convert to a mixed number if desired.

Q2: Can this calculator handle negative numbers?
A: No, this version only accepts positive integers. Negative numbers would require additional handling of the sign.

Q3: What's the largest number this calculator can handle?
A: It depends on your server's PHP configuration, but typically up to 2^31-1 (2,147,483,647) for 32-bit systems.

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

Q5: Can I simplify more than one fraction at a time?
A: This calculator simplifies one fraction at a time. For multiple fractions, you would need to submit each separately.