Fraction Calculator
Fraction Arithmetic
About Fraction Calculator
Working with Fractions
Fractions represent parts of a whole and are fundamental to mathematics, cooking, construction, and countless everyday applications. A fraction consists of a numerator (top number) and denominator (bottom number). While the concept is simple, performing arithmetic operations with fractions requires specific rules that many people find challenging. This calculator handles all four basic operations and automatically simplifies results to their lowest terms, saving you from tedious manual calculation and potential errors.
Fraction Arithmetic Rules
Addition and subtraction require a common denominator: find the LCD, adjust numerators, then add or subtract. a/b + c/d = (ad + bc) / bd. Multiplication is straightforward: multiply numerators together and denominators together. a/b x c/d = ac/bd. Division flips the second fraction and multiplies: a/b / c/d = a/b x d/c = ad/bc. After each operation, the result is reduced to lowest terms by dividing both parts by their greatest common divisor.
How to Use This Calculator
Enter the numerator and denominator for each fraction, select the operation (add, subtract, multiply, or divide), and click Calculate. The result shows both the unsimplified answer and the simplified form. Mixed numbers are supported: enter the whole number, numerator, and denominator separately. The calculator also converts results between improper fractions and mixed numbers automatically.
Frequently Asked Questions
How do I simplify a fraction?
Find the greatest common divisor (GCD) of the numerator and denominator, then divide both by it. For example, 12/18: GCD is 6, so 12/18 = 2/3.
What is an improper fraction?
An improper fraction has a numerator larger than its denominator (like 7/4). It can be converted to a mixed number by dividing: 7/4 = 1 and 3/4.
Why do I need a common denominator for addition?
You can only add pieces of the same size. Different denominators mean different-sized pieces. Converting to a common denominator makes all pieces the same size so they can be combined.
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