Exact fraction math
Add, subtract, multiply, or divide fractions and mixed numbers. Simplify to lowest terms, convert decimals to fractions, and follow the calculation steps.
Results
Calculate with two fractions using all four arithmetic operations, or simplify a fraction or finite decimal on its own. Exact answers appear in lowest terms. The decimal and percentage are convenient representations, not replacements for the exact fraction.
The numerator is the number above the fraction bar. The denominator is the number below. A fraction such as 3/4 describes three equal parts of a whole divided into four parts. The denominator cannot be zero. A fraction with numerator larger than denominator is called improper, and it can also be written as a mixed number.
Use a common denominator, change the numerators to matching equivalent fractions, then combine the numerators. Reduce the resulting fraction by the greatest common divisor. For example, 1/6 + 1/4 becomes 2/12 + 3/12 = 5/12. Do not simply add denominators.
For multiplication, multiply the numerators and multiply the denominators, then simplify. For example, 2/3 × 9/10 = 18/30 = 3/5. For division, multiply by the second fraction's reciprocal. Division by zero is undefined and produces an input error, not an infinite result.
A mixed number combines a whole part and a proper fraction, such as 2 1/3. Convert to an improper fraction before calculating. A minus sign applies to the entire mixed value: -2 1/3 means -7/3, not -2 + 1/3. For example, -2 1/3 + 1/3 = -2.
To simplify a fraction, divide numerator and denominator by their greatest common divisor. A finite decimal uses a power-of-ten denominator before reducing: 2.75 = 275/100 = 11/4 = 2 3/4. The entered 0.333333333333 is an exact finite decimal and is not inferred to equal the repeating fraction 1/3.
All arithmetic and reduction use integer fraction math. Terminating decimals are shown exactly when they fit in 12 decimal places. Repeating decimals are clearly marked approximate, for example 1/3 ≈ 0.333333333333. Tiny nonzero fractions keep their exact value even when a short decimal would round to zero.
Calculations run in your browser page, not a cloud math service. Work is not saved or uploaded. Inputs allow at most 30 numeric digits, ordinary decimals up to 12 decimal places, and absolute values through one trillion. Other algebraic tasks, including partial fraction decomposition, are outside this calculator.
Guide
Review the four arithmetic rules, how mixed numbers work, and how to reduce a fraction.
