Simplify Improper Fraction Calculator

Improper Fraction Simplification:

\[ \frac{a}{b} = \left\lfloor\frac{a}{b}\right\rfloor + \frac{a \bmod b}{b} \quad \text{if} \quad a > b \] \[ \text{Simplified form:} \quad \frac{a/g}{b/g} \]

Simplified Fraction:

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1. What is an Improper Fraction?

An improper fraction is a fraction where the numerator (top number) is greater than or equal to the denominator (bottom number). Examples include 5/2, 7/3, or 4/4. These can be converted to mixed numbers (combinations of whole numbers and proper fractions).

2. How to Simplify Fractions

To simplify a fraction:

\[ \frac{a}{b} = \frac{a \div g}{b \div g} \]

Where \( g \) is the greatest common divisor (GCD) of \( a \) and \( b \). The GCD is the largest number that divides both numerator and denominator without leaving a remainder.

3. Converting to Mixed Numbers

For improper fractions (\( a > b \)):

\[ \frac{a}{b} = \left\lfloor\frac{a}{b}\right\rfloor + \frac{a \bmod b}{b} \]

This converts the improper fraction to a mixed number consisting of a whole number and a proper fraction.

4. Using the Calculator

Instructions: Enter the numerator and denominator (both must be positive integers). The calculator will show the simplified fraction and, if applicable, the mixed number form.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between simplifying and converting to mixed numbers?
A: Simplifying reduces the fraction to lowest terms, while converting to mixed numbers separates the whole number part from the fractional part.

Q2: Do all improper fractions have mixed number equivalents?
A: Yes, any improper fraction can be expressed as a mixed number or whole number.

Q3: What if my fraction is already in simplest form?
A: The calculator will show the same fraction, just confirmed to be simplified.

Q4: Can this calculator handle negative fractions?
A: No, this calculator only works with positive integers for numerator and denominator.

Q5: What's the largest number this calculator can handle?
A: It depends on your server's PHP configuration, but typically up to 2 billion for 32-bit systems.