Adding & Subtracting Negative Fractions Calculator

Negative Fractions Formula:

\[ \left(-\frac{a}{b}\right) + \left(-\frac{c}{d}\right) = -\frac{a \times d + b \times c}{b \times d} \]

First Fraction Numerator (a):

First Fraction Denominator (b):

Second Fraction Numerator (c):

Second Fraction Denominator (d):

Operation:

Result:

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1. What is Negative Fractions Addition/Subtraction?

Adding and subtracting negative fractions follows the same rules as positive fractions, with additional attention to sign rules. When both fractions are negative, the result remains negative.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \left(-\frac{a}{b}\right) + \left(-\frac{c}{d}\right) = -\frac{a \times d + b \times c}{b \times d} \]

For subtraction:

\[ \left(-\frac{a}{b}\right) - \left(-\frac{c}{d}\right) = -\frac{a \times d - b \times c}{b \times d} \]

Where:

\( a, c \) — Numerators (can be positive or negative)
\( b, d \) — Denominators (must be positive)

Explanation: The calculator finds a common denominator, performs the operation on numerators, and simplifies the result.

3. Importance of Negative Fractions

Details: Negative fractions appear in many real-world applications like physics (vectors), finance (losses), and temperature changes. Understanding their arithmetic is fundamental in algebra.

4. Using the Calculator

Tips: Enter numerators and denominators (denominators must be positive). Select addition or subtraction operation. The calculator will simplify the result automatically.

5. Frequently Asked Questions (FAQ)

Q1: What if denominators are different?
A: The calculator automatically finds the common denominator (product of denominators) before performing the operation.

Q2: How are negative signs handled?
A: The calculator maintains proper sign rules - two negatives make a positive in subtraction.

Q3: What if I enter a negative denominator?
A: Denominators are treated as positive (absolute value) since negative denominators are typically standardized.

Q4: How is simplification performed?
A: The result is simplified by dividing numerator and denominator by their greatest common divisor (GCD).

Q5: What if the result is positive?
A: The calculator will show a positive result if that's the mathematically correct outcome.