Consider the binary oeration * : R × R → R defined as a*b = a + b / 2

$a*b=\frac{a+b}{2}$, so $b*a=\frac{a+b}{2}$ → commulative

$(a*b)*c=\frac{\frac{a+b}{2}+c}{2}$

$a*(b*c)=\frac{a+\frac{b+c}{2}}{2}$

$=\frac{a+b+2c}{4}=\frac{2a+b+c}{4}$ → not associative as $(a*b)*c≠a*(b*c)$