I have a simple question about quotient group operations. To this end, if $\displaystyle K$ is a normal subgroup of $\displaystyle G$, then $\displaystyle G/K$ is group under the binary operation defined by $\displaystyle (g_{1}K)*(g_{2}K)=(g_{1}g_{2})K$. This is all I have in my notes.

So, my question is: if the “mother group” $\displaystyle G$ is an additive group, then do we have that $\displaystyle (g_{1}K)*(g_{2}K)=(g_{1}+g_{2})K$?

Thanks