Math
Fraction Calculator
Add, subtract, multiply, or divide two fractions. Shows simplified results, decimal equivalents, and mixed number form.
Enter numerators and denominators above (denominators cannot be 0)
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Fraction Operation Formulas
Addition: a/b + c/d = (ad + bc) / bd
Subtraction: a/b − c/d = (ad − bc) / bd
Multiplication: a/b × c/d = ac / bd
Division: a/b ÷ c/d = ad / bc
All results are reduced using the Greatest Common Divisor (GCD) algorithm.
How to Use This Calculator
Choose an operation (add, subtract, multiply, or divide), then enter the numerator and denominator of each fraction. Denominators cannot be zero.
The result shows the unsimplified form, the fully simplified fraction, the decimal equivalent, and the mixed number if the result is an improper fraction.
Frequently asked questions
How do you add fractions with different denominators?
Find a common denominator by multiplying the two denominators together. Then convert each fraction and add the numerators: a/b + c/d = (ad + bc) / bd. Finally, simplify by dividing by the GCD.
How do you divide fractions?
To divide fractions, multiply the first fraction by the reciprocal of the second: a/b ÷ c/d = a/b × d/c = ad / bc.
What does simplifying a fraction mean?
Simplifying means dividing both the numerator and denominator by their greatest common divisor (GCD) until no common factor remains. For example, 6/8 simplifies to 3/4 because GCD(6, 8) = 2.
What is a mixed number?
A mixed number combines a whole number and a proper fraction, for example 1 3/4. It is the equivalent of an improper fraction where the numerator is larger than the denominator.
What is the difference between a proper and improper fraction?
A proper fraction has a numerator smaller than its denominator (e.g. 3/4). An improper fraction has a numerator equal to or greater than its denominator (e.g. 7/4), and can be rewritten as a mixed number.