Why is the rate of disappearance negative?
Reaction rates are generally by convention given based on the formation of the product, and thus reaction rates are positive. So, for the reaction:

$$\ce{A-&gt;B}$$

$$\text{Rate} = \frac{\Delta[\ce{B}]}{\Delta t}$$

To ensure that you get a positive reaction rate, the rate of disappearance of reactant has a negative sign:

$$\text{Rate} = -\frac{\Delta[\ce{A}]}{\Delta t}=\frac{\Delta[\ce{B}]}{\Delta t}$$