Fraction Calculator — Add, Subtract, Multiply, Divide Fractions
Calculate fractions with step-by-step simplification. Add, subtract, multiply, or divide any two fractions and get the result as a simplified fraction and decimal. See also Fraction to Decimal and Decimal to Fraction.
How to Calculate Fractions
To calculate with fractions, you need to understand the four basic operations. For addition and subtraction, find a common denominator first, then add or subtract the numerators. For multiplication, multiply the numerators together and the denominators together. For division, flip the second fraction (reciprocal) and multiply. After computing, always simplify the result by dividing both numerator and denominator by their greatest common divisor (GCD).
Fraction Formulas
Addition: a/b + c/d = (a×d + c×b) / (b×d)
Subtraction: a/b − c/d = (a×d − c×b) / (b×d)
Multiplication: a/b × c/d = (a×c) / (b×d)
Division: a/b ÷ c/d = (a×d) / (b×c)
Simplify: divide numerator and denominator by GCD
Worked Example
1/2 + 1/3 = ?
Step 1: Find common denominator: 2 × 3 = 6
Step 2: Convert: 1/2 = 3/6, 1/3 = 2/6
Step 3: Add numerators: 3 + 2 = 5
Result: 5/6 ≈ 0.8333
Frequently Asked Questions
How do you add fractions with different denominators?
Find the least common denominator (LCD), convert each fraction to an equivalent fraction with that denominator, then add the numerators. For example, 1/4 + 1/6: LCD = 12, so 3/12 + 2/12 = 5/12.
What does it mean to simplify a fraction?
Simplifying (or reducing) a fraction 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.
How do you divide fractions?
To divide fractions, multiply the first fraction by the reciprocal (flipped version) of the second. For example, 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6.
Can fractions have negative numbers?
Yes. A fraction is negative if either the numerator or denominator (but not both) is negative. This calculator handles negative values and always places the sign on the numerator in the simplified result.