Rate of reaction and rate constant confusion

If we had the reaction,
$A + B$ $\rightarrow$ $C$, and $A$ was second order, and $B$ was first order, we would say that $rate = k[A]^2[B]$, but this has confused me. When we say $rate$, do we mean the rate of change of the concentration of the products, or the reactants, and if it is reactants, why is it not negative (as the reactants are decreasing wrt time)
Thanks for the help in advance




If $A$ is a reactant, the rate $r$ of the reaction consuming $A$ is defined by : $r$ = - ${d[A]/dt}$. Take care of the *minus* sign !


If the reaction is second-order in $A$ and first order in $B$ the rate is expressed by the following expression : $$r = - {d[A]/dt}= k [A]^2[B]$$


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