Signed Fraction Division Calculator With Solution

Fraction Division Formula:

\[ \frac{a}{b} \div \frac{c}{d} = \frac{a \times d}{b \times c} \]

First Fraction Sign:

First Fraction Numerator (a):

First Fraction Denominator (b):

Second Fraction Sign:

Second Fraction Numerator (c):

Second Fraction Denominator (d):

Result:

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1. What is Fraction Division?

Fraction division involves dividing one fraction by another. The operation is equivalent to multiplying the first fraction by the reciprocal of the second fraction. The sign of the result follows the same rules as multiplication (positive if signs are the same, negative if different).

2. How Does the Calculator Work?

The calculator uses the fraction division formula:

\[ \frac{a}{b} \div \frac{c}{d} = \frac{a \times d}{b \times c} \]

Where:

\( \frac{a}{b} \) — First fraction
\( \frac{c}{d} \) — Second fraction
The sign of the result is determined by multiplying the signs of the input fractions

3. Rules for Signed Fractions

Sign Rules:

(+) ÷ (+) = +
(-) ÷ (-) = +
(+) ÷ (-) = -
(-) ÷ (+) = -

4. Using the Calculator

Tips: Enter numerators and denominators as integers. Denominator cannot be zero. The calculator will show step-by-step solution including sign determination and simplification.

5. Frequently Asked Questions (FAQ)

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

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

Q3: What if the result is a whole number?
A: The calculator will show it as a fraction with denominator 1 (e.g., 5/1).

Q4: Can I enter negative numerators/denominators?
A: The sign should be selected separately. Enter absolute values for numerators and denominators.

Q5: What about mixed numbers?
A: Convert mixed numbers to improper fractions before using the calculator.