1. What is This Calculator For?

This calculator performs basic arithmetic operations (addition, subtraction, multiplication, division) between two fractions represented by variables (x/y) and (z/w). All variables are unitless.

2. How Does the Calculator Work?

The calculator uses standard fraction arithmetic:

Where:

• \( x \) — Numerator of first fraction
• \( y \) — Denominator of first fraction (cannot be zero)
• \( z \) — Numerator of second fraction
• \( w \) — Denominator of second fraction (cannot be zero)
• \( op \) — Selected operation (+, -, ×, ÷)

3. Understanding the Operations

Addition: \(\frac{x}{y} + \frac{z}{w} = \frac{xw + zy}{yw}\)
Subtraction: \(\frac{x}{y} - \frac{z}{w} = \frac{xw - zy}{yw}\)
Multiplication: \(\frac{x}{y} \times \frac{z}{w} = \frac{xz}{yw}\)
Division: \(\frac{x}{y} \div \frac{z}{w} = \frac{xw}{yz}\)

4. Using the Calculator

Tips: Enter values for all four variables (x, y, z, w). Denominators (y and w) must not be zero. Select the desired operation from the dropdown menu.

5. Frequently Asked Questions (FAQ)

Q1: What happens if I enter zero for y or w?
A: The calculator will prevent division by zero by requiring y and w to be greater than zero.

Q2: Can I use negative numbers?
A: Yes, the calculator accepts negative values for x and z (numerators).

Q3: How precise are the results?
A: Results are rounded to 4 decimal places for readability.

Q4: What's the difference between this and a regular fraction calculator?
A: This calculator uses variables to represent the numerator and denominator, making it more flexible for algebraic applications.

Q5: Can I use this for complex fractions?
A: This calculator handles simple fractions. For complex fractions, you may need to break them down into simpler components first.