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 that is easier to work with and understand.

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 compare, add, subtract, multiply, and divide. They provide the most reduced form of a fraction, which is often required in mathematical solutions and final answers.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What if I enter a fraction that's already simplified?
A: The calculator will return the same fraction with a GCD of 1.

Q2: Can this calculator handle improper fractions?
A: Yes, it works with both proper and improper fractions.

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).

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

Q5: Can I simplify fractions with decimal numbers?
A: This calculator only works with integers. For decimals, multiply by a power of 10 to convert to integers first.