$P$ and $Q$ represent numbers, and $P \ast Q$ means $\cfrac{P+Q}{2}$. What is the value of $3 \ast (6 \ast 8)$?
This problem involves a non-standard operation, so I need to be careful not to confuse it with regular multiplication. I can start by simplifying the expression inside the parentheses, using the definition of $\ast$. So, $6 \ast 8$ means $\cfrac{6+8}{2}$, which is $7$. Now I have $3 \ast 7$, which means $\cfrac{3+7}{2}$. That is $5$. So the value of the expression is $5$. 