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 principle:

Where:

• \( a \) — Numerator (unitless)
• \( b \) — Denominator (unitless)
• \( g \) — Greatest Common Divisor of a and b (unitless)

Explanation: The calculator first 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 understand, compare, and use in further calculations. They represent the most reduced form of a fraction while maintaining the same value.

4. Using the Calculator

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

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

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

Q4: How is the GCD calculated?
A: Using the Euclidean algorithm, an efficient method for finding the GCD of two numbers.

Q5: Can I simplify improper fractions?
A: Yes, the calculator works with both proper and improper fractions.