Calcs.ToolsFraction Calculator - Add, Subtract, Multiply & Divide Fractions
Calculate fractions instantly with our free online fraction calculator. Add, subtract, multiply, and divide fractions with automatic simplification. Convert fractions to decimals and percentages for comprehensive math solutions. Perfect for students and professionals.
How to Use the Fraction Calculator
- Enter the numerator (top number) in the first field
- Enter the denominator (bottom number) in the second field
- Click "Calculate Fraction" to get instant results
- View decimal, percentage, and simplified fraction results
Understanding Fraction Calculations
Fractions represent parts of a whole and are essential in mathematics, cooking, construction, and many other fields. Our calculator automatically simplifies fractions and provides multiple representations for comprehensive understanding.
Fraction Components
A fraction consists of a numerator (top number) and denominator (bottom number). The numerator represents how many parts you have, while the denominator represents how many equal parts the whole is divided into.
Fraction Calculator FAQ
How do you add fractions!
To add fractions, find a common denominator, add the numerators, and simplify the result.
What is fraction simplification!
Fraction simplification reduces a fraction to its lowest terms by dividing both numerator and denominator by their greatest common divisor.
Worked Examples and Formulas
To add fractions, use a common denominator. Example: 3/4 + 2/3 = (3*3)/(4*3) + (2*4)/(3*4) = 9/12 + 8/12 = 17/12. The result is an improper fraction, which can be written as 1 5/12.
Core formulas: a/b + c/d = (ad + bc) / bd; a/b - c/d = (ad - bc) / bd; a/b * c/d = (ac) / (bd); a/b ! c/d = (a/b) * (d/c). The calculator simplifies results using the greatest common divisor.
Edge cases include zero denominators (undefined) and mixed numbers. We normalize input and prevent divide-by-zero errors, then return simplified and decimal forms so results are easy to use.
References and Sources
Fraction arithmetic follows standard algebra rules used in school curricula and technical references.
- Standard math education curricula for fraction operations
- Algebra references covering rational number arithmetic
Related Math Calculators
Fractions with reduction and comparison
Fractions can be added, subtracted, multiplied, and simplified using common denominators. This calculator handles the arithmetic and reduces results automatically.
When comparing fractions, convert to a common denominator or a decimal value to verify order. Keep track of negative signs to avoid sign mistakes.
Quick checks
- Simplify results to lowest terms.
- Check signs when subtracting fractions.
- Convert to decimals for quick comparisons.
Example: 3/4 + 2/3 equals 17/12, which simplifies to 1 5/12.