Mixed Number Calculator - Add, Subtract, Multiply, Divide
Perform arithmetic on mixed numbers with step-by-step results. Add, subtract, multiply, or divide any two mixed fractions and get the answer as a simplified mixed number.
Enter the whole number, numerator, and denominator for each mixed number, choose an operation, and click Calculate.
Mixed Number Calculator - Add, Subtract, Multiply, Divide
Perform arithmetic on mixed numbers with step-by-step results. Add, subtract, multiply, or divide any two mixed fractions and get the answer as a simplified mixed number.
Mixed Number 1
Mixed Number 2
About the mixed number calculator
A mixed number combines a whole-number part with a proper fraction part — for example, 2¾ (two and three-quarters) or 5⅓ (five and one-third). Mixed numbers appear constantly in cooking recipes, carpentry measurements, and any context where quantities fall between whole units. Arithmetic on mixed numbers by hand requires several careful steps, and errors are easy to make. This calculator handles all four operations — addition, subtraction, multiplication, and division — and simplifies the result into the lowest-terms mixed number automatically.
The algorithm works in three stages. First, each mixed number is converted to an improper fraction: multiply the whole part by the denominator, then add the numerator, keeping the same denominator. So 2¾ becomes (2×4 + 3)/4 = 11/4, and 1½ becomes (1×2 + 1)/2 = 3/2. Second, the appropriate arithmetic rule is applied to the two improper fractions. For addition and subtraction, both fractions must be brought to a common denominator (using the least common multiple) before the numerators are combined. For multiplication, the numerators multiply together and the denominators multiply together. For division, the first fraction is multiplied by the reciprocal (flip) of the second. Third, the resulting improper fraction is reduced to lowest terms using the greatest common divisor, and then converted back to a mixed number if the absolute value of the numerator exceeds the denominator.
Working with negative mixed numbers is straightforward: a negative mixed number such as −2¾ is treated as the improper fraction −11/4 throughout. The sign of the result follows the standard rules of signed arithmetic.
This calculator is useful for students learning fraction arithmetic, home cooks scaling recipes (doubling 1¾ cups, splitting 3½ teaspoons), woodworkers calculating lumber lengths, and anyone else who needs reliable mixed-number arithmetic without pen and paper. Each result is shown as both an improper fraction and a mixed number so you can verify the conversion and use whichever form is most convenient.
Note that the input fields accept whole numbers only. If you want to calculate with proper fractions alone (no whole part), simply enter 0 for the whole-number field. Similarly, if one of your mixed numbers is a whole number with no fraction, enter 0 for the numerator.
Mixed number calculator examples
Real-world scenarios demonstrating each arithmetic operation.
| Operation | Result | Context |
|---|---|---|
| 2 1/2 + 1 1/4 | 3 3/4 | Adding lengths: two-and-a-half metres plus one-and-a-quarter metres equals three-and-three-quarter metres. |
| 3 1/2 − 1 3/4 | 1 3/4 | Subtracting ingredients: 3½ cups minus 1¾ cups leaves 1¾ cups. |
| 1 3/4 × 2 | 3 1/2 | Doubling a recipe: 1¾ cups of sugar doubled gives 3½ cups. |
| 12 1/4 ÷ 3 1/2 | 3 1/2 | Dividing lumber: a 12¼-foot plank divided into 3½-foot pieces yields exactly 3.5 pieces. |
How to use the mixed number calculator
- Select the arithmetic operation you want to perform: Add, Subtract, Multiply, or Divide.
- Enter the whole number, numerator, and denominator for the first mixed number. For a pure fraction enter 0 for the whole; for a whole number enter 0 for the numerator.
- Enter the same three fields for the second mixed number.
- Click Calculate. The result appears as both an improper fraction and a simplified mixed number, along with the conversion steps.
- Click Reset to clear all inputs and start a new calculation.
Mixed number calculator FAQ
What is a mixed number?
A mixed number consists of a whole-number part and a proper fraction part written side by side — for example, 3½. The fraction part must be proper (numerator less than denominator). Mixed numbers are used whenever a quantity is greater than one whole unit but not an exact whole number.
How do I convert a mixed number to an improper fraction?
Multiply the whole number by the denominator, then add the numerator, and place the result over the original denominator. For 2¾: (2 × 4) + 3 = 11, so 2¾ = 11/4. This is the essential first step in any mixed-number arithmetic and the calculator performs it automatically.
How are the fractions added or subtracted?
After converting both mixed numbers to improper fractions, the calculator finds the least common denominator (LCD) of the two denominators, rewrites each fraction over the LCD, and then adds or subtracts the numerators. The result is then simplified and converted back to a mixed number.
How does multiplication and division work?
For multiplication, numerators are multiplied together and denominators are multiplied together: (a/b) × (c/d) = (a×c)/(b×d). For division, the first fraction is multiplied by the reciprocal of the second: (a/b) ÷ (c/d) = (a/b) × (d/c) = (a×d)/(b×c). The result is simplified before conversion.
Can I enter negative mixed numbers?
To enter a negative mixed number, enter a negative value for the whole number field (e.g., −2) and keep the numerator and denominator positive. The calculator treats the entire mixed number as negative and handles the sign arithmetic correctly through all four operations.
What does 'simplified' mean in this context?
A fraction is in simplified (lowest-terms) form when the greatest common divisor of the numerator and denominator is 1. For example, 6/8 simplifies to 3/4 because GCD(6,8) = 2. The calculator always reduces results to lowest terms so you get the cleanest possible answer.