1. What is Fraction Reduction?

Fraction reduction simplifies a fraction to its lowest terms by dividing both numerator and denominator by their greatest common divisor (GCD). This produces 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 reduces the fraction:

Example: For 8/12, GCD is 4 → 8÷4/12÷4 = 2/3

3. Importance of Lowest Terms

Details: Reduced fractions are standard in mathematics, making comparisons easier and calculations simpler. They represent the most simplified form of a ratio.

4. Using the Calculator

Tips: Enter positive integers for numerator and denominator. The calculator will return the fraction in its simplest form or the same fraction if already reduced.

5. Frequently Asked Questions (FAQ)

Q1: What if I enter a numerator larger than denominator?
A: The calculator works for improper fractions (like 5/2) and will reduce them if possible.

Q2: Can this handle negative numbers?
A: This version only accepts positive integers. Negative values would require sign handling.

Q3: What about fractions with zero?
A: Denominator cannot be zero (undefined). Numerator zero always results in 0/1.

Q4: How is this different from decimal conversion?
A: This preserves the exact fractional form rather than converting to decimal approximation.

Q5: What's the largest number this can handle?
A: Limited by PHP's integer size (typically up to 2^31-1 or 2^63-1 on 64-bit systems).