If @$(A,B)$ denotes the average of $A$ and $B$, /$(A,B)$ denotes the product of $A$ and $B$, and $\times(A,B)$ denotes $A$ divided by $B$, which expression represents the sum of $A$ and $B$?

Since @$(A,B)=\dfrac{A+B}{2}$, multiplying this by 2 gives $A+B$. The notation /$(X,2)$ means product of $X$ and 2, so $/(@(A,B),2)=\dfrac{A+B}{2}\times 2=A+B$. The other expressions do not simplify to the sum in general.