1. What is a Fraction Calculator?

The Fraction Calculator computes the decimal value and simplified form of a fraction given its numerator and denominator. It helps in understanding and working with fractional values in mathematics.

2. How Does the Calculator Work?

The calculator uses the following calculations:

Where:

• \( a \) — Numerator (integer)
• \( b \) — Denominator (positive integer)
• \( \gcd(a,b) \) — Greatest common divisor of a and b

Explanation: The calculator first computes the decimal value by simple division, then simplifies the fraction by dividing both numerator and denominator by their greatest common divisor.

3. Importance of Fraction Calculation

Details: Understanding fractions is fundamental in mathematics. Simplified fractions are easier to work with in equations and comparisons, while decimal forms are often more intuitive for real-world applications.

4. Using the Calculator

Tips: Enter any integer for the numerator and a positive integer for the denominator. The calculator will show both the decimal equivalent and the simplified fraction form.

5. Frequently Asked Questions (FAQ)

Q1: What if I enter 0 for the denominator?
A: The calculator requires a non-zero denominator as division by zero is undefined in mathematics.

Q2: How does the simplification work?
A: The calculator finds the greatest common divisor (GCD) of the numerator and denominator, then divides both by this number.

Q3: What about negative fractions?
A: Negative signs can be placed on either the numerator or denominator (but not both). The simplified form will show the negative sign on the numerator.

Q4: What if the fraction is already in simplest form?
A: The calculator will return the same fraction as the simplified version.

Q5: How precise is the decimal conversion?
A: The decimal is rounded to 4 decimal places for readability while maintaining reasonable precision.