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Fraction Operations:
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Fraction operations involve performing arithmetic calculations (addition, subtraction, multiplication, and division) with fractions. This calculator helps you perform these operations accurately and shows results in both fractional and decimal forms.
The calculator performs the following operations:
Addition: \[ \frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd} \]
Subtraction: \[ \frac{a}{b} - \frac{c}{d} = \frac{ad - bc}{bd} \]
Multiplication: \[ \frac{a}{b} \times \frac{c}{d} = \frac{ac}{bd} \]
Division: \[ \frac{a}{b} \div \frac{c}{d} = \frac{ad}{bc} \]
Explanation: The calculator first performs the operation using fraction rules, then simplifies the result by finding the greatest common divisor (GCD).
Details: Understanding fraction operations is fundamental in mathematics and essential for many real-world applications including measurements, ratios, and proportional relationships.
Tips: Enter numerators and denominators for both fractions, select the operation, and click calculate. The calculator will show the result in three forms: original fraction, simplified fraction, and decimal equivalent.
Q1: Why can't I enter zero for denominators?
A: Division by zero is undefined in mathematics, so denominators must be non-zero values.
Q2: How does the simplification work?
A: The calculator uses the Euclidean algorithm to find the greatest common divisor (GCD) of the numerator and denominator, then divides both by this value.
Q3: Can I enter negative numbers?
A: Yes, you can enter negative numbers for numerators. The calculator will properly handle negative values in the results.
Q4: What if my result is an improper fraction?
A: The calculator shows the result as-is. Improper fractions (where numerator > denominator) are mathematically valid.
Q5: How precise are the decimal results?
A: Decimal results are rounded to 4 decimal places for readability, but calculations are performed with full precision.