1. What Is This Equation?

This calculator demonstrates the equivalence between two forms of expressing the multiplication of 2 by a mixed number (1 3/x). The equation shows how to simplify such expressions.

2. How Does the Calculator Work?

The calculator evaluates both sides of the equation:

Where:

• \( x \) — Any positive real number (cannot be zero)
• 2 — The multiplier
• 1 3/x — The mixed number being multiplied

3. Mathematical Explanation

Details: The mixed number 1 3/x is equivalent to 1 + 3/x. When multiplied by 2, it becomes 2 × (1 + 3/x). The right side shows the simplified form after distributing the multiplication.

4. Using the Calculator

Tips: Enter any positive value for x to see how both sides of the equation evaluate to the same result, demonstrating their equivalence.

5. Frequently Asked Questions (FAQ)

Q1: Why does x have to be positive?
A: x cannot be zero (division by zero is undefined) and negative values would make the fraction negative, which complicates the mixed number interpretation.

Q2: What is a mixed number?
A: A mixed number combines a whole number and a proper fraction, like 1 3/4 (which equals 1.75).

Q3: How is this useful in real-world applications?
A: Understanding these transformations is fundamental in algebra and appears in various calculations involving rates, ratios, and proportional relationships.

Q4: Why do both sides always give the same result?
A: Because they are mathematically equivalent expressions - the right side is just a simplified version of the left side.

Q5: Can this be extended to other numbers besides 2 and 1 3/x?
A: Yes, the same principle applies to any similar expression: n × (a b/x) = [n × (a × x + b)]/x.