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Fraction Operation:
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This calculator performs arithmetic operations (addition, subtraction, multiplication, division) on fractions represented by variables (x/y) and (z/w). It provides results in both fractional and decimal forms.
The calculator performs the selected operation according to standard fraction arithmetic rules:
Addition: \[ \frac{x}{y} + \frac{z}{w} = \frac{x \times w + z \times y}{y \times w} \]
Subtraction: \[ \frac{x}{y} - \frac{z}{w} = \frac{x \times w - z \times y}{y \times w} \]
Multiplication: \[ \frac{x}{y} \times \frac{z}{w} = \frac{x \times z}{y \times w} \]
Division: \[ \frac{x}{y} \div \frac{z}{w} = \frac{x \times w}{y \times z} \]
Explanation: The calculator first performs the operation according to these rules, then simplifies the resulting fraction by finding the greatest common divisor.
Details: Fraction operations are fundamental in mathematics, physics, engineering, and many real-world applications where ratios and proportions are involved.
Tips: Enter values for all variables (x, y, z, w). Denominators (y and w) must be non-zero. The calculator will show the operation result in three forms: original fraction, simplified fraction, and decimal equivalent.
Q1: What happens if I enter zero for a denominator?
A: The calculator requires non-zero denominators. Division by zero is mathematically undefined.
Q2: How does the simplification work?
A: The calculator finds the greatest common divisor (GCD) of the numerator and denominator and divides both by this value.
Q3: Can I use negative numbers?
A: Yes, the calculator handles negative values for all variables except denominators.
Q4: What's the precision of the decimal result?
A: The decimal result is rounded to 4 decimal places for readability.
Q5: Can I use this for complex fractions?
A: This calculator handles simple fractions. For complex fractions (fractions within fractions), additional steps would be needed.