Add, subtract, multiply or divide fractions instantly. This free fraction calculator simplifies every answer to lowest terms and shows it as a mixed number, decimal and percentage.
Enter a numerator and denominator for each fraction, pick an operation, and see the simplified result, mixed number and decimal.
Adds, subtracts, multiplies and divides fractions, then reduces to lowest terms using the greatest common divisor. Handles negative numbers and improper fractions.
How the Fraction Calculator Works
This tool adds, subtracts, multiplies or divides two fractions and always reduces the answer to lowest terms, so you never have to simplify by hand. Enter a numerator and denominator for each fraction, choose an operation, and it works out the result along with its mixed number, decimal and percentage equivalents.
Formula: Addition: (n1 × d2 + n2 × d1) ÷ (d1 × d2). Subtraction: (n1 × d2 − n2 × d1) ÷ (d1 × d2). Multiplication: (n1 × n2) ÷ (d1 × d2). Division: (n1 × d2) ÷ (d1 × n2). Whichever operation you pick, the calculator then divides both the resulting numerator and denominator by their greatest common divisor (GCD) to reduce the fraction to lowest terms.
- n1 / d1 — the numerator and denominator of the first fraction
- Operation — addition (+), subtraction (−), multiplication (×) or division (÷)
- n2 / d2 — the numerator and denominator of the second fraction
Example Scenarios
| Fraction 1 | Operation | Fraction 2 | Result (simplified) |
|---|---|---|---|
| 1/2 | + | 1/3 | 5/6 |
| 3/4 | − | 1/4 | 1/2 |
| 2/3 | × | 3/5 | 2/5 |
| 1/2 | ÷ | 1/4 | 2 |
| 5/6 | + | 1/6 | 1 |
| 7/8 | − | 3/8 | 1/2 |
Fraction Calculator FAQ
How does the calculator simplify fractions to lowest terms?
It finds the greatest common divisor (GCD) of the resulting numerator and denominator, then divides both by that GCD. For example a raw result of 6/15 has a GCD of 3, so it simplifies to 2/5.Can I enter negative numbers in a fraction?
Yes, either the numerator or denominator can be negative. The calculator handles the sign correctly and shows the simplified result with the sign on the numerator.Does it work with improper fractions where the numerator is bigger than the denominator?
Yes, improper fractions like 7/4 are fully supported, and the result panel also shows the equivalent mixed number, such as 1 and 3/4, alongside the simplified fraction.Why does dividing fractions flip the second one?
Dividing by a fraction is mathematically the same as multiplying by its reciprocal, so the calculator computes (n1 × d2) ÷ (d1 × n2) — swapping n2 and d2 — instead of dividing straight across.What’s the difference between the mixed number and decimal results?
The mixed number shows the result as a whole number plus a leftover fraction (useful for measurements), while the decimal converts the same value into base-10 form (useful for calculations), such as 1 and 3/4 versus 1.75.How do I read my fraction result as a percentage?
The Percentage field converts the simplified result directly into a percent by multiplying the decimal value by 100, so 1/2 shows as 50%.Related Calculators
If you just need to reduce a single fraction rather than combine two, the fraction simplifier does that directly. For related number-theory tasks, the LCM calculator and GCF calculator find the least common multiple and greatest common factor behind the scenes of fraction simplification, and the ratio calculator is useful when you’re comparing two quantities instead of combining fractions.