Signed Fraction Division Calculator Mixed Numbers

Mixed Numbers Division Formula:

\[ \left(\pm a \frac{b}{c}\right) \div \left(\pm d \frac{e}{f}\right) = \left(\pm \frac{(a \times c) + b}{c}\right) \times \left(\pm \frac{f}{(d \times f) + e}\right) \]

First Fraction Sign:

First Whole Number:

First Numerator:

First Denominator:

Second Fraction Sign:

Second Whole Number:

Second Numerator:

Second Denominator:

Division Result:

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1. What is Mixed Numbers Division?

Mixed numbers division involves dividing two numbers that each consist of a whole number and a proper fraction, with consideration for positive or negative signs. The process requires converting mixed numbers to improper fractions, handling the signs, and then multiplying by the reciprocal of the divisor.

2. How Does the Calculator Work?

The calculator uses the following steps:

\[ \left(\pm a \frac{b}{c}\right) \div \left(\pm d \frac{e}{f}\right) = \left(\pm \frac{(a \times c) + b}{c}\right) \times \left(\pm \frac{f}{(d \times f) + e}\right) \]

Where:

\( a \frac{b}{c} \) — First mixed number
\( d \frac{e}{f} \) — Second mixed number
\( \pm \) — Positive or negative sign

Explanation: The calculator first converts mixed numbers to improper fractions, determines the sign of the result, multiplies by the reciprocal, and simplifies the result.

3. Importance of Signed Fractions

Details: Proper handling of signs in fraction operations is crucial in algebra, physics, and engineering applications where direction or polarity matters.

4. Using the Calculator

Tips: Enter whole numbers, numerators and denominators for both fractions. Select appropriate signs (+ or -). Denominators must be positive integers.

5. Frequently Asked Questions (FAQ)

Q1: What if my denominator is zero?
A: The calculator requires denominators to be positive integers. Division by zero is undefined.

Q2: How are negative fractions handled?
A: The sign applies to the entire mixed number. Negative divided by negative gives positive result.

Q3: What if my numerator is larger than denominator?
A: The calculator will properly convert the improper fraction to a mixed number in the result.

Q4: Can I divide by a whole number?
A: Yes, just enter the whole number with numerator 0 and denominator 1.

Q5: How is the result simplified?
A: The calculator reduces the result to lowest terms using greatest common divisor.