Explain the relation between the rate of reaction and the stoichiometric coefficients of a balanced chemical equation with examples.

For a general chemical reaction $aA + bB \rightarrow cC + dD$,the rate of reaction is defined by dividing the rate of change of concentration of each species by its respective stoichiometric coefficient.
Rate of reaction $= -\frac{1}{a} \frac{\Delta[A]}{\Delta t} = -\frac{1}{b} \frac{\Delta[B]}{\Delta t} = \frac{1}{c} \frac{\Delta[C]}{\Delta t} = \frac{1}{d} \frac{\Delta[D]}{\Delta t}$
Example $1$: For the reaction $2HI_{(g)} \rightarrow H_{2(g)} + I_{2(g)}$
Rate $= -\frac{1}{2} \frac{\Delta[HI]}{\Delta t} = \frac{\Delta[H_2]}{\Delta t} = \frac{\Delta[I_2]}{\Delta t}$
Example $2$: For the reaction $2NH_{3(g)} \rightarrow N_{2(g)} + 3H_{2(g)}$
Rate $= -\frac{1}{2} \frac{\Delta[NH_3]}{\Delta t} = \frac{\Delta[N_2]}{\Delta t} = \frac{1}{3} \frac{\Delta[H_2]}{\Delta t}$