Math Tools
Fraction
Calculator
Add, subtract, multiply, divide, and simplify fractions with complete step-by-step solutions. Supports mixed numbers, improper fractions, and decimal conversion.
Add fractionsSubtractMultiplyDivideSimplifyMixed numbers
Add Two Fractions
+
Result
5
6
=
0.8333…
Step-by-Step Solution
How to Work with Fractions
Fractions represent a part of a whole. The number above the line (numerator) represents the parts taken, and below (denominator) represents the total equal parts. This calculator handles all four arithmetic operations and simplification, showing every step clearly.
Fraction Operation Formulas
Addition/Subtraction: a/b ± c/d = (a×d ± c×b) / (b×d)
Then simplify by dividing by GCD(numerator, denominator)
Multiplication: a/b × c/d = (a×c) / (b×d)
Division: a/b ÷ c/d = a/b × d/c = (a×d) / (b×c)
Simplify: a/b → divide both by GCD(a,b)
What is a mixed number?
A mixed number combines a whole number and a proper fraction, like 2½. To convert to an improper fraction: multiply the whole number by the denominator and add the numerator. So 2½ = (2×2+1)/2 = 5/2. This calculator accepts both mixed numbers and improper fractions.
What is LCD and why is it used?
LCD stands for Least Common Denominator — the smallest number divisible by both denominators. It's needed when adding or subtracting fractions with different denominators. For example, to add 1/4 + 1/6, the LCD is 12. Convert: 3/12 + 2/12 = 5/12. Using LCD keeps numbers smaller and simplification easier than just multiplying denominators.
Can a denominator be zero?
No. Division by zero is undefined in mathematics. A fraction with a denominator of zero (e.g., 5/0) has no value. This is because there is no number that you can multiply 0 by to get 5. The calculator will show an error if you enter a zero denominator.