Is it a convention to divide rate of reaction by stoichiometric coefficient?

If we consider a reaction


$$ \ce{A + B -> 3 C} $$


The rate of reaction is given by


$$ R= -\dfrac{\Delta[A]}{\Delta t} = -\dfrac{\Delta[B]}{\Delta t} = \frac13\dfrac{\Delta[C]}{\Delta t} $$


I know we divide it by $3$ for equality, but we can also multiply $3$ in other two concentrations too, right? Then the result will be:


$$ R= -\dfrac{3\Delta[A]}{\Delta t} = -\dfrac{3\Delta[B]}{Δt}=\dfrac{\Delta[C]}{\Delta t}$$


So is it just a convention to divide instead of multiplication?


