1. What is Simplifying Proper Fractions?

Simplifying proper fractions means reducing them to their lowest terms by dividing both numerator and denominator by their greatest common divisor (GCD). A proper fraction has a numerator smaller than its denominator.

2. How Does the Calculator Work?

The calculator uses the following formula:

Where:

• \( \gcd(a, b) \) — Greatest common divisor of a and b
• Numerator — Top number of the fraction (must be less than denominator)
• Denominator — Bottom number of the fraction

Explanation: The calculator finds the GCD of numerator and denominator, then divides both by this number to get the simplified form.

3. Importance of Simplifying Fractions

Details: Simplified fractions are easier to work with in calculations and comparisons. They represent the same value in their most reduced form.

4. Using the Calculator

Tips: Enter positive integers for numerator and denominator. The numerator must be less than the denominator for proper fractions. The calculator will display the simplified form or an error message if inputs are invalid.

5. Frequently Asked Questions (FAQ)

Q1: What is a proper fraction?
A: A proper fraction has a numerator smaller than its denominator (e.g., 3/4 is proper, 5/4 is improper).

Q2: How do you find the GCD?
A: The GCD is the largest number that divides both numerator and denominator without a remainder. We use the Euclidean algorithm.

Q3: What if my fraction is already simplified?
A: The calculator will return the same fraction (e.g., input 1/2 returns 1/2).

Q4: Can I simplify improper fractions with this?
A: No, this calculator is specifically for proper fractions. For improper fractions, you might convert to mixed numbers first.

Q5: What about negative fractions?
A: This calculator works with positive proper fractions only.