Fraction Calculator
The fraction calculator performs all four basic arithmetic operations on fractions: addition, subtraction, multiplication, and division. Enter two fractions and select the operation, and the calculator returns the result in both simplified fraction form and as a decimal. The calculator automatically finds the greatest common divisor (GCD) to reduce fractions to lowest terms. All intermediate steps are shown to help you understand how the calculation works. Whether you need to add 1/2 + 1/3, multiply 2/5 * 3/4, or divide 1/2 / 2/3, this calculator handles it instantly with full simplification.
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
Common fraction operations
| Operation | Calculation | Result | Decimal |
|---|---|---|---|
| 1/2 + 1/3 | 3/6 + 2/6 | 5/6 | 0.833... |
| 3/4 - 1/4 | 3/4 - 1/4 | 2/4 = 1/2 | 0.50 |
| 1/2 * 2/3 | 2/6 | 1/3 | 0.333... |
| 1/2 / 2/3 | 3/4 | 3/4 | 0.75 |
| 5/6 + 1/6 | 6/6 | 1 | 1.00 |
Common denominators, and when a fraction beats a decimal
Adding or subtracting fractions is really one problem: giving them a common denominator so the pieces are the same size. You cannot add thirds and quarters until both are twelfths, and skipping that step is the classic fraction error. Multiplication and division are gentler: multiply straight across, and to divide, flip the second fraction and multiply.
The deeper point is that a fraction is often more honest than its decimal. One third is exact; 0.33 is rounded, and the small error it introduces can accumulate through a calculation or surface when you multiply back. That is why recipes, gear ratios, construction measurements and music keep working in fractions: they express exact proportions that decimals only approximate. Reduce a fraction to its lowest terms to read it clearly, but reach for the decimal only when you need to compare sizes at a glance or feed a value into a tool that expects one.
Fraction calculator: frequently asked questions
How do I add fractions?
To add fractions with the same denominator, add the numerators and keep the denominator: 1/4 + 2/4 = 3/4. To add fractions with different denominators, find the least common multiple (LCM) of the denominators, convert each fraction to use the LCM, then add the numerators. For example, 1/2 + 1/3 = 3/6 + 2/6 = 5/6.
How do I subtract fractions?
Subtraction works the same as addition. With the same denominator, subtract the numerators: 3/4 - 1/4 = 2/4 = 1/2. With different denominators, find a common denominator first. For example, 1/2 - 1/3 = 3/6 - 2/6 = 1/6.
How do I multiply fractions?
Multiply the numerators together and the denominators together: (a/b) * (c/d) = (a*c) / (b*d). For example, 1/2 * 2/3 = 2/6 = 1/3. Always simplify the result using the GCD.
How do I divide fractions?
To divide fractions, multiply the first fraction by the reciprocal of the second: (a/b) / (c/d) = (a/b) * (d/c) = (a*d) / (b*c). For example, 1/2 / 2/3 = 1/2 * 3/2 = 3/4.
What does it mean to simplify a fraction?
Simplifying a fraction means reducing it to lowest terms by dividing both numerator and denominator by their greatest common divisor (GCD). For example, 6/8 simplifies to 3/4 because GCD(6,8) = 2, and 6/2 = 3, 8/2 = 4.
Official sources
- Standard mathematical formulas for fraction arithmetic.
- NIST Special Publication 330: The International System of Units.
Reviewed by the CalculatorHub team, edited by James Graham, 14 June 2026. See our methodology.