Math Suite

Fraction Calculator

Add, subtract, multiply, and divide fractions and mixed numbers. Get the simplified fraction and its decimal equivalent instantly.

Understanding Fractions and Their Operations

Fractions represent a part of a whole or, more generally, any number of equal parts. Whether you are scaling a recipe, measuring building materials, or solving complex algebraic equations, a solid grasp of fractional mathematics is essential. Our fraction calculator simplifies the process by automatically finding common denominators, performing the requested operation, and reducing the result to its simplest form.

Core Fractional Operations

  • Addition & Subtraction: To add or subtract fractions, they must have a common denominator. The calculator automatically determines the Least Common Multiple (LCM) of the denominators before combining the numerators.
  • Multiplication: Multiplying fractions is straightforward-simply multiply the numerators together to get the new numerator, and multiply the denominators together to get the new denominator.
  • Division: To divide by a fraction, the calculator multiplies the first fraction by the reciprocal (the inverse) of the second fraction.

The Mathematical Logic

Simplifying a fraction involves dividing both the numerator and the denominator by their Greatest Common Divisor (GCD). Our algorithm uses the Euclidean algorithm to quickly compute the GCD and yield a fraction in its lowest, most readable terms:

Simplified Numerator = Numerator ÷ GCD(Numerator, Denominator)
Simplified Denominator = Denominator ÷ GCD(Numerator, Denominator)

FAQ

There is an optional 'Whole' input box next to each fraction. If you leave it blank, the calculator assumes it is 0 and only uses the numerator and denominator.
Yes, the calculator automatically simplifies the final fraction to its lowest terms and converts improper fractions into mixed numbers.
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