Fraction Calculator
Add, subtract, multiply, or divide fractions and get the answer simplified, with a decimal equivalent.
About the Fractions Calculator
Fraction arithmetic requires finding common denominators for addition and subtraction, or cross-multiplying for division — easy to fumble by hand. This calculator performs all four basic operations on two fractions and automatically simplifies the result to lowest terms, plus shows the decimal equivalent.
How It Works
For addition and subtraction, the calculator cross-multiplies to find a common denominator before combining numerators. For multiplication, it multiplies numerators and denominators directly. For division, it multiplies by the reciprocal of the second fraction. The result is then simplified by dividing both numerator and denominator by their greatest common divisor.
Addition: a/b + c/d = (ad+bc)/bd. Subtraction: (ad−bc)/bd. Multiplication: ac/bd. Division: ad/bc. Simplified by dividing by GCD.
Worked example
Scenario: Adding 1/2 and 1/3.
- Common denominator: 2 × 3 = 6.
- Convert: 1/2 = 3/6 and 1/3 = 2/6.
- Add numerators: 3 + 2 = 5, giving 5/6 (≈ 0.8333).
Result: 1/2 + 1/3 = 5/6.
Understanding the fraction result
Fractions describe parts of a whole. A result can be written as a simplified fraction, an improper fraction, a mixed number, or a decimal. Simplifying does not change the value: 6/8 and 3/4 represent the same quantity. For addition and subtraction, fractions first need a common denominator; multiplication and division use different rules.
Tips and common mistakes
- Results are always reduced to lowest terms, and improper fractions also show a mixed number (7/4 + 1/3 = 2 1/12).
- Enter mixed numbers as improper fractions: 1 3/4 = 7/4.
- Numerators and denominators must be whole numbers; denominators can't be zero.
Assumptions & Limitations
- Assumes both denominators entered are nonzero, since division by zero is undefined.
- Automatically handles a negative result by keeping the negative sign on the numerator, not the denominator.
- Works with two fractions at a time — for three or more fractions, combine them two at a time in sequence.