Fraction Calculator – Add, Subtract, Multiply & Divide Fractions
Our free fraction calculator makes it easy to add, subtract, multiply, and divide any two fractions in seconds. Whether you're helping with homework or solving everyday math problems, this tool instantly returns a fully simplified fraction, decimal equivalent, and mixed number. Just enter your fractions, choose an operation, and get the answer along with a clear step-by-step solution.
Enter the top number of the first fraction.
Enter the bottom number of the first fraction. Cannot be zero.
Select the arithmetic operation to perform.
Enter the top number of the second fraction.
Enter the bottom number of the second fraction. Cannot be zero.
Your results will appear here
How to Use This Calculator
1. Enter the numerator (top number) of the first fraction in the 'Numerator 1' field. 2. Enter the denominator (bottom number) of the first fraction in the 'Denominator 1' field — make sure it is not zero. 3. Choose the operation you want to perform: Add, Subtract, Multiply, or Divide. 4. Enter the numerator and denominator of the second fraction in the respective fields. 5. Click 'Calculate' to instantly see the simplified fraction result, the decimal equivalent, the mixed number form, and a step-by-step breakdown of how the answer was reached.
How Fraction Arithmetic Works
A fraction represents a part of a whole and is written as numerator/denominator. The numerator is the number on top and the denominator is the number on the bottom. Performing arithmetic on fractions follows specific rules depending on the operation.
Adding and Subtracting Fractions
To add or subtract fractions, you need a common denominator. The simplest approach is to use the product of both denominators as a common denominator:
- Addition: (a/b) + (c/d) = (a×d + c×b) / (b×d)
- Subtraction: (a/b) − (c/d) = (a×d − c×b) / (b×d)
After computing the result, simplify by dividing both the numerator and denominator by their Greatest Common Divisor (GCD).
Multiplying Fractions
Multiplying fractions is straightforward — multiply the numerators together and the denominators together:
- Multiplication: (a/b) × (c/d) = (a×c) / (b×d)
Then simplify the resulting fraction to its lowest terms.
Dividing Fractions
To divide fractions, multiply the first fraction by the reciprocal (the flipped version) of the second fraction:
- Division: (a/b) ÷ (c/d) = (a/b) × (d/c) = (a×d) / (b×c)
Simplify the result as usual.
Simplifying Fractions (Lowest Terms)
A fraction is in its simplest form when the GCD of the numerator and denominator is 1. To simplify, find the GCD using the Euclidean algorithm and divide both parts by it. For example, 6/8 simplifies to 3/4 because GCD(6,8) = 2.
Mixed Numbers
When the absolute value of the numerator is greater than the denominator (an improper fraction), it can be expressed as a mixed number. For example, 7/4 = 1 3/4. The whole part is the integer quotient and the remainder becomes the new numerator.