1. What Are Proper Fractions?

A proper fraction is a fraction where the numerator (top number) is less than the denominator (bottom number). Examples include 1/2, 3/4, and 7/8. These represent quantities less than one whole unit.

2. How Fraction Calculation Works

The calculator performs several operations on proper fractions:

Key calculations:

• Simplification: Divides numerator and denominator by their greatest common divisor (GCD)
• Decimal conversion: Calculates the decimal equivalent by division
• Validation: Ensures the fraction is proper (a < b)

3. Importance of Proper Fractions

Details: Proper fractions are fundamental in mathematics, representing parts of a whole. They're essential in probability, ratios, measurements, and many real-world applications.

4. Using the Calculator

Tips: Enter positive integers for numerator and denominator. The numerator must be smaller than the denominator. The calculator will simplify the fraction and show its decimal equivalent.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between proper and improper fractions?
A: Proper fractions have numerators smaller than denominators (value < 1), while improper fractions have numerators equal to or larger than denominators (value ≥ 1).

Q2: How is the greatest common divisor (GCD) calculated?
A: Using the Euclidean algorithm which repeatedly divides the larger number by the smaller number until the remainder is zero.

Q3: Can I enter negative numbers?
A: No, this calculator only works with positive integers for proper fractions.

Q4: What if my fraction can't be simplified?
A: The calculator will show the original fraction as the simplified form (e.g., 2/3 is already in simplest form).

Q5: Why is the decimal value rounded?
A: The decimal is rounded to 4 decimal places for readability, though the exact value could be a repeating decimal.