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Here are some practice exercises involving multiplication and division with mixed numbers. The expectation is that readers can make these calculations here without a calculator.

Divide: $3\,\frac{3}{4}\div-2\,\frac{1}{2}\text{.}$

Multiply: $-1\frac{2}{5}\cdot-2\frac{1}{3}\text{.}$

Solution

Since we are dividing numbers of opposite signs, the answer is negative and
$\begin{aligned} 3\,\frac{3}{4}\div-2\,\frac{1}{2}\amp=\frac{15}{4}\div-\frac{5}{2}\\ \amp=-\frac{3}{2}\\ \amp=-1\,\frac{1}{2}\text{.} \end{aligned}$

Since we are multiplying two negative numbers, the answer is positive and
$\begin{aligned} -1\frac{2}{5}\cdot-2\frac{1}{3}\amp=-\frac{7}{5}\cdot-\frac{7}{3}\\ \amp=\frac{49}{15}\\ \amp=3\,\frac{4}{15}\text{.} \end{aligned}$

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