Fraction Bar Calculator Wolfram Formula

Wolfram Formula for Fraction Operations:

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

First Fraction:

Operation:

Second Fraction:

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 fractions using the standard mathematical formulas. It provides results in both original and simplified forms.

2. How Does the Calculator Work?

The calculator uses standard fraction operations formulas:

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

Explanation:

For addition/subtraction, find a common denominator by multiplying denominators
For multiplication, multiply numerators and denominators directly
For division, multiply by the reciprocal of the second fraction
Results are automatically simplified by dividing by the greatest common divisor (GCD)

3. Importance of Fraction Operations

Details: Understanding fraction operations is fundamental in mathematics, with applications in algebra, calculus, physics, engineering, and everyday measurements. Proper fraction manipulation is essential for accurate calculations.

4. Using the Calculator

Tips: Enter numerators and denominators for both fractions, select the operation, and click Calculate. The calculator will show the result in original form and simplified form (if different).

5. Frequently Asked Questions (FAQ)

Q1: What if I enter 0 as a denominator?
A: Division by zero is undefined. The calculator requires non-zero denominators.

Q2: How are negative fractions handled?
A: The negative sign can be placed on either numerator or denominator. The calculator will properly simplify them.

Q3: Does the calculator show decimal equivalents?
A: No, this calculator focuses on exact fractional results. For decimal conversions, use a separate tool.

Q4: What's the maximum size of numbers supported?
A: The calculator uses standard PHP integer limits, typically up to 2 billion for 32-bit systems.

Q5: Can I use this for mixed numbers?
A: Convert mixed numbers to improper fractions first (e.g., 1½ becomes 3/2).