Answer
false
Work Step by Step
RECALL:
The Multiplication Properties of Inequality state that when a negative number is multiplied to each side of an inequality, the inequality sign changes to the opposite direction.
Since $c$ is negative, then $\frac{1}{c}$ will also be negative.
Thus, if $a\lt b$. then multiplying a negative number $\frac{1}{c}$ to each side of this inequality gives:
$\begin{array}{ccc}
&a &\lt &b
\\&a \cdot \frac{1}{c} &\gt &b \cdot \frac{1}{c}
\\&\frac{a}{c} &\gt &\frac{b}{c}
\end{array}$
Therefore, the given statement is false.