Fraction Bar Calculator Mathway Algebra

Algebraic Fraction Calculator:

\[ \frac{a}{b} \pm \frac{c}{d} = \frac{ad \pm bc}{bd} \] \[ \frac{a}{b} \times \frac{c}{d} = \frac{ac}{bd} \] \[ \frac{a}{b} \div \frac{c}{d} = \frac{ad}{bc} \]

First Fraction Numerator:

First Fraction Denominator:

Operation:

Second Fraction Numerator:

Second Fraction Denominator:

Result:

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1. What is the Fraction Bar Calculator?

The Fraction Bar Calculator performs basic arithmetic operations (addition, subtraction, multiplication, and division) on algebraic fractions. It provides results in both unsimplified and simplified forms.

2. How Does the Calculator Work?

The calculator uses standard fraction operations:

\[ \text{Addition: } \frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd} \] \[ \text{Subtraction: } \frac{a}{b} - \frac{c}{d} = \frac{ad - bc}{bd} \] \[ \text{Multiplication: } \frac{a}{b} \times \frac{c}{d} = \frac{ac}{bd} \] \[ \text{Division: } \frac{a}{b} \div \frac{c}{d} = \frac{ad}{bc} \]

Explanation: The calculator first performs the operation according to these rules, then simplifies the result by finding the greatest common divisor (GCD).

3. Importance of Fraction Operations

Details: Understanding fraction operations is fundamental in algebra and higher mathematics. Fractions appear in equations, ratios, proportions, and many real-world applications.

4. Using the Calculator

Tips: Enter numerators and denominators for both fractions, select the operation. Denominators cannot be zero. Results are shown in both original and simplified forms.

5. Frequently Asked Questions (FAQ)

Q1: What if I get a negative denominator?
A: The calculator automatically moves the negative sign to the numerator for standard form (e.g., 1/-2 becomes -1/2).

Q2: How does simplification work?
A: The calculator finds the greatest common divisor (GCD) of numerator and denominator and divides both by it.

Q3: Can I enter negative fractions?
A: Yes, you can enter negative values for either numerator or denominator.

Q4: What if I divide by zero?
A: The calculator will not accept zero as a denominator for either input fraction.

Q5: Does this work for mixed numbers?
A: No, this calculator only works with simple fractions. Convert mixed numbers to improper fractions first.