Fractions Calculator

Fraction Operations:

\[ \frac{a}{b} \text{ op } \frac{c}{d} = \text{result} \]

Numerator 1 (a):

Denominator 1 (b):

Operation:

Numerator 2 (c):

Denominator 2 (d):

Result:

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1. What is the Fractions Calculator?

The Fractions Calculator performs basic arithmetic operations (addition, subtraction, multiplication, and division) on two fractions. It provides results in both original and simplified forms.

2. How Does the Calculator Work?

The calculator performs the following operations:

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

Where:

\( a \) — Numerator of first fraction
\( b \) — Denominator of first fraction
\( c \) — Numerator of second fraction
\( d \) — Denominator of second fraction

Explanation: The calculator automatically simplifies the result by finding the greatest common divisor (GCD) of the numerator and denominator.

3. Importance of Fraction Operations

Details: Understanding fraction operations is fundamental in mathematics, with applications in measurements, ratios, probabilities, and real-world problem solving.

4. Using the Calculator

Tips: Enter numerators and denominators (must be integers, denominators cannot be zero), select an operation, and click Calculate. The result will show in both original and simplified forms if applicable.

5. Frequently Asked Questions (FAQ)

Q1: What if I enter a zero denominator?
A: The calculator requires denominators to be positive integers. It will not accept zero denominators.

Q2: How does the simplification work?
A: The calculator uses the Euclidean algorithm to find the greatest common divisor (GCD) and divides both numerator and denominator by this value.

Q3: Can I enter negative fractions?
A: Yes, you can enter negative numerators. The negative sign should be on the numerator.

Q4: What if the result is a whole number?
A: The calculator will show the fractional form and the simplified whole number form (e.g., "4/2 = 2").

Q5: Does it handle improper fractions?
A: Yes, the calculator works with both proper and improper fractions.