Multiplying Mixed Numbers

To multiply mixed numbers, turn each one into an improper fraction first. Take 2 and 1/2 times 1 and 1/3. 2 and 1/2 is $\frac{5}{2}$, and 1 and 1/3 is $\frac{4}{3}$. Now it is an ordinary product of fractions: $\frac{5}{2}\cdot \frac{4}{3}$ is $\frac{20}{6}$, which simplifies to $\frac{10}{3}$.

The classic mistake is to multiply the wholes and the fractions separately: 2 times 1 is 2, and 1/2 times 1/3 is 1/6, giving 2 and 1/6. That answer is far too small, because it skips half the work. Picture a rectangle 2 and 1/2 long and 1 and 1/3 wide: it splits into four pieces, whole by whole, whole by fraction, fraction by whole and fraction by fraction. The shortcut counts only two of them.

Adding mixed numbers part by part works because a sum can be regrouped. A product of two sums cannot, so convert first and the problem is safe.