What this calculator does
The Multiply Mixed Numbers Calculator multiplies two mixed numbers — numbers written as a whole part plus a fraction, such as 2 1/2 or 1 1/3. It returns the answer as a fully simplified fraction, as a mixed number, and as a decimal, so you can use whichever form your homework or project requires.
How to use it
Enter the whole number, numerator, and denominator for each mixed number. If a value is a pure fraction, leave the whole part as 0. If it is a whole number, set the numerator to 0 and the denominator to 1. Press calculate to see the product. Denominators of zero are treated as 1 to avoid division errors.
The formula explained
First, each mixed number is converted to an improper fraction using \(A\,b/c = (A \cdot c + b)/c\). Then the two improper fractions are multiplied straight across: multiply the numerators together and the denominators together. Finally the result is reduced by dividing both top and bottom by their greatest common divisor (GCD), and converted back to a mixed number.
$$\left(\text{W}_1 + \frac{\text{N}_1}{\text{D}_1}\right) \times \left(\text{W}_2 + \frac{\text{N}_2}{\text{D}_2}\right) = \frac{n_1 \cdot n_2}{\text{D}_1 \cdot \text{D}_2}$$$$\text{where}\quad \left\{ \begin{aligned} n_1 &= \text{W}_1 \cdot \text{D}_1 \pm \text{N}_1 \\ n_2 &= \text{W}_2 \cdot \text{D}_2 \pm \text{N}_2 \end{aligned} \right.$$
Worked example
Multiply \(2\,1/2 \times 1\,1/3\). Convert: \(2\,1/2 = 5/2\) and \(1\,1/3 = 4/3\). Multiply: $$\frac{5 \times 4}{2 \times 3} = \frac{20}{6}.$$ Simplify by dividing by GCD 2: \(10/3\). As a mixed number that is \(3\,1/3\), and as a decimal about \(3.3333\).
FAQ
Can I multiply more than two numbers? This tool handles two at a time; multiply the first pair, then re-enter the result against the third number.
What about negative mixed numbers? Enter a negative whole number; the calculator applies the sign to the whole fraction correctly.
Why convert to improper fractions? You cannot simply multiply whole parts and fractional parts separately — converting to a single fraction gives the correct product every time.
