1. What is Fraction Simplification?

Fraction simplification (reducing to lowest terms) means dividing both numerator and denominator by their greatest common divisor (GCD) to obtain an equivalent fraction with the smallest possible whole numbers.

2. How Does the Calculator Work?

The calculator uses the Euclidean algorithm to find GCD:

Then divides both numerator and denominator by the GCD:

3. Importance of Lowest Terms

Details: Simplified fractions are easier to work with in calculations, comparisons, and provide the most reduced form for clear communication of fractional quantities.

4. Using the Calculator

Tips: Enter positive integers for both numerator and denominator. The calculator will show the simplified form and the divisor used.

5. Frequently Asked Questions (FAQ)

Q1: What if I enter a fraction already in lowest terms?
A: The calculator will return the same fraction with "(divided by 1)" indicating no reduction was needed.

Q2: Can this handle improper fractions?
A: Yes, the calculator works with any positive fraction regardless of whether numerator is larger than denominator.

Q3: What about mixed numbers?
A: Convert to improper fraction first (e.g., 2 1/2 becomes 5/2), then simplify if needed.

Q4: How does this relate to decimal equivalents?
A: Simplified fractions have the same decimal value as the original, just in reduced form.

Q5: What's the largest number this can handle?
A: Limited by PHP's integer size (typically up to 2,147,483,647 on 32-bit systems).