Fraction Calculator
Add, subtract, multiply, or divide two fractions and see every step: the common denominator, the invert-and-multiply rule, and the GCD simplification. Results are shown as an improper fraction, a mixed number, and a decimal.
Two fractions
First fraction
Operation
Second fraction
1/2 + 1/3 = 5/6
Common denominator: LCM(2, 3) = 6
1/2 = (1 × 3)/6 = 3/6
1/3 = (1 × 2)/6 = 2/6
3/6 + 2/6 = 5/6
5/6 is already in lowest terms (GCD = 1)
5/6
Improper fraction
5/6
Mixed number
0.833333
Decimal
Frequently Asked Questions
- How do I add fractions with different denominators?
- Rewrite both fractions over a common denominator (the least common multiple of the two denominators), then add the numerators. For example, 1/2 + 1/3 = 3/6 + 2/6 = 5/6.
- How do I multiply fractions?
- Multiply straight across: numerator times numerator, denominator times denominator. For example, 2/3 × 3/4 = 6/12, which simplifies to 1/2.
- How do I divide fractions?
- Invert the second fraction and multiply. Dividing by 3/4 is the same as multiplying by 4/3, so 1/2 ÷ 3/4 = 1/2 × 4/3 = 4/6 = 2/3.
- How do I simplify a fraction?
- Divide the numerator and denominator by their greatest common divisor (GCD). For 6/12, the GCD is 6, so 6/12 simplifies to 1/2.
- What is a mixed number?
- A mixed number combines a whole number and a proper fraction, like 1 3/4. It equals the improper fraction 7/4. This calculator shows results both ways, plus the decimal value.
- Why can't the denominator be zero?
- A fraction means division, and division by zero is undefined. The calculator rejects zero denominators, and when dividing it also rejects a second fraction with a zero numerator, since the inverted fraction would have zero on the bottom.