Determine which of the following binary operations on the set $N$ are associative and which are commutative. $a * b = \frac{a+b}{2}$ for all $a, b \in N$.

(N/A) For commutativity,we check if $a * b = b * a$ for all $a, b \in N$.
$a * b = \frac{a+b}{2} = \frac{b+a}{2} = b * a$.
Since $a * b = b * a$,the operation is commutative.
For associativity,we check if $(a * b) * c = a * (b * c)$ for all $a, b, c \in N$.
$(a * b) * c = \left(\frac{a+b}{2}\right) * c = \frac{\frac{a+b}{2} + c}{2} = \frac{a+b+2c}{4}$.
$a * (b * c) = a * \left(\frac{b+c}{2}\right) = \frac{a + \frac{b+c}{2}}{2} = \frac{2a+b+c}{4}$.
Since $\frac{a+b+2c}{4} \neq \frac{2a+b+c}{4}$ in general,the operation is not associative.