Calculator With Fractions and Negative

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 Numerator (a):

First Fraction Denominator (b):

Operation:

Second Fraction Numerator (c):

Second Fraction Denominator (d):

Result:

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1. What is Fraction Calculator?

This calculator performs basic arithmetic operations (addition, subtraction, multiplication, and division) on fractions, including those with negative values. It also simplifies the results to their lowest terms.

2. How Does the Calculator Work?

The calculator uses standard fraction arithmetic rules:

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

After calculation, the result is simplified by dividing both numerator and denominator by their greatest common divisor (GCD).

3. Handling Negative Numbers

Details: Negative numbers can be entered in either numerator or denominator. The calculator follows standard sign rules:

\(\frac{-a}{b} = -\frac{a}{b}\)
\(\frac{a}{-b} = -\frac{a}{b}\)
\(\frac{-a}{-b} = \frac{a}{b}\)

4. Using the Calculator

Tips: Enter numerators and denominators for both fractions, select the operation, and click Calculate. The calculator will show the raw result and simplified form.

5. Frequently Asked Questions (FAQ)

Q1: What if I enter zero in denominator?
A: The calculator will show an error as division by zero is undefined.

Q2: How are negative results displayed?
A: The negative sign appears with the numerator in simplified form.

Q3: What's the maximum number size?
A: Limited by PHP's integer size (typically ±2 billion).

Q4: Does it handle mixed numbers?
A: No, enter as improper fractions (e.g., 1½ as 3/2).

Q5: How is simplification performed?
A: Using the Euclidean algorithm to find GCD.