Multiplying Mixed Numbers

There are two main tricks for multiplying mixed numbers.

1. FOILing: You can treat the mixed numbers as binomials and FOIL them. For $(A + \frac{b}{c})(D + \frac{e}{f})$, the result is $AD + A\frac{e}{f} + D\frac{b}{c} + (\frac{b}{c})(\frac{e}{f})$. This works best when the whole numbers are easily divisible by the denominators.

2. Special Case: If the whole numbers are the same ($n$) and the fractional parts sum to 1, the result is simple. The whole part of the answer is $n(n+1)$, and the fractional part is the product of the two fractions. For example, $9\frac{1}{3} \times 9\frac{2}{3} = 9(10) + (\frac{1}{3})(\frac{2}{3}) = 90\frac{2}{9}$.

Sometimes, converting to improper fractions and simplifying is the easiest method.