1. What is Fraction Simplification?

Fraction simplification is the process of reducing a fraction to its simplest form where the numerator and denominator have no common divisors other than 1. For example, 12/15 simplifies to 4/5.

2. How Does the Calculator Work?

The calculator uses the greatest common divisor (GCD) method:

Where:

• \( a \) — Numerator
• \( b \) — Denominator
• \( \text{GCD}(a,b) \) — Greatest common divisor of a and b

Example: For 12/15, GCD is 3, so we divide both by 3 to get 4/5.

3. Importance of Simplified Fractions

Details: Simplified fractions are easier to work with in calculations and comparisons. They represent the same value in a more compact form and are the standard way to express fractional answers.

4. Using the Calculator

Tips: Enter any numerator and denominator (positive integers) to see the simplified form. The calculator will show the simplified fraction and the divisor used.

5. Frequently Asked Questions (FAQ)

Q1: What if my fraction can't be simplified?
A: If the GCD is 1, the fraction is already in simplest form (e.g., 4/5).

Q2: Can this calculator handle improper fractions?
A: Yes, it works for both proper and improper fractions (e.g., 15/12 → 5/4).

Q3: What about mixed numbers?
A: Convert to improper fraction first (e.g., 1 3/12 → 15/12 → 5/4).

Q4: How is the GCD calculated?
A: Using the Euclidean algorithm which efficiently finds the largest number that divides both numerator and denominator.

Q5: Can I simplify negative fractions?
A: This calculator uses absolute values, but normally the negative sign would be placed on the numerator or in front of the fraction.