What is the Mixed Number Calculator?
A mixed number combines a whole number with a proper fraction, such as 2½. This calculator lets you add, subtract, multiply, or divide two mixed numbers (or plain fractions) and returns the answer as a simplified fraction, a mixed number, and a decimal. It works for negative whole numbers too.
How to use it
Enter the whole, numerator, and denominator for each value, pick an operation, and submit. For a plain fraction like ¾, set the whole part to 0. For a whole number like 5, set numerator 0 and denominator 1. Denominators of zero are treated as 1 to avoid errors.
The formula explained
Each mixed number is first converted to an improper fraction using (whole × denominator + numerator) / denominator. The chosen operation is applied with cross-multiplication: addition and subtraction use a common denominator (q·s), multiplication multiplies tops and bottoms, and division multiplies by the reciprocal. The final fraction is reduced by dividing the numerator and denominator by their greatest common divisor (GCD).
$$\frac{A}{B} + \frac{C}{D} = \frac{A\,D + C\,B}{B\,D}$$ $$\text{where}\quad \left\{ \begin{aligned} \frac{A}{B} &= \text{Whole 1} + \frac{\text{Num 1}}{\text{Den 1}} \\ \frac{C}{D} &= \text{Whole 2} + \frac{\text{Num 2}}{\text{Den 2}} \end{aligned} \right.$$
Worked example
Compute 2½ + 1¾. Convert: 2½ = 5/2 and 1¾ = 7/4. Common denominator: 5/2 = 10/4, so 10/4 + 7/4 = 17/4. As a mixed number that is 4¼, and as a decimal 4.25.
$$2\tfrac{1}{2} + 1\tfrac{3}{4} = \frac{5}{2} + \frac{7}{4} = \frac{10}{4} + \frac{7}{4} = \frac{17}{4} = 4\tfrac{1}{4} = 4.25$$FAQ
Can I use negative numbers? Yes — put the minus sign on the whole-number field; the sign carries through the whole fraction.
What if the result is a whole number? You'll see it as a fraction over 1 (for example \(\frac{4}{1}\)) plus the mixed and decimal forms.
Does it always simplify? Yes, the result is reduced to lowest terms using the GCD automatically.
