1. What is a Mixed Number?

A mixed number combines a whole number and a proper fraction (where the numerator is less than the denominator). It's an alternative way to represent improper fractions or decimal numbers that include both integer and fractional parts.

2. How Does the Calculator Work?

The calculator converts decimal numbers to mixed numbers using the following approach:

Where:

• Whole Number — The integer part of the decimal
• Numerator/Denominator — The simplified fractional part

3. Conversion Process

Step 1: Separate the whole number part from the decimal part.
Step 2: Convert the decimal part to a fraction using continued fractions algorithm.
Step 3: Simplify the resulting fraction by dividing numerator and denominator by their greatest common divisor (GCD).
Step 4: Combine the whole number with the simplified fraction.

4. Using the Calculator

Tips: Enter any decimal number (positive or negative). The calculator will automatically convert it to the simplest mixed number form.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between a mixed number and an improper fraction?
A: A mixed number shows the whole and fractional parts separately (e.g., 2 1/2), while an improper fraction has a numerator larger than the denominator (e.g., 5/2).

Q2: Can all decimals be converted to exact fractions?
A: Only terminating and repeating decimals can be converted to exact fractions. Irrational numbers can only be approximated.

Q3: How accurate is the conversion?
A: The calculator uses a tolerance of 1×10⁻⁶ for approximation, providing very accurate results for most practical purposes.

Q4: What about negative numbers?
A: The negative sign applies to the entire mixed number (e.g., -1.75 becomes -1 3/4).

Q5: Why would I need to use mixed numbers?
A: Mixed numbers are often easier to understand and work with in real-world measurements (like cooking or construction) than improper fractions or decimals.