Rate of disappearance is given as $-\frac{\Delta [A]}{\Delta t}$ where $\ce{A}$ is a reactant. However, using this formula, the rate of disappearance cannot be negative.
$\Delta [A]$ will be negative, as $[A]$ will be lower at a later time, since it is being used up in the reaction. Then, $[A]_{\text{final}} - [A]_{\text{initial}}$ will be negative. Therefore, the numerator in $-\frac{\Delta [A]}{\Delta t}$ will be negative.
$\Delta t$ will be positive because final time minus initial time will be positive.
This means that $-\frac{\Delta [A]}{\Delta t}$ will evaluate to $(-)\frac{(-)}{(+)} = (-) \cdot (-) =(+)$
However, we still write the rate of disappearance as a negative number. Also, if you think about it, a negative rate of disappearance is essentially a positive rate of appearance. The reactants disappear at a positive rate, so why isn't the rate of disappearance positive?