The operation * is defined on the set of real numbers by a*b=a+b+ab/2. Is the operation associative

we check that (a*b)*c = a*(b*c) 

(a*b)*c = (a+b+ab/2)*c = 
a+b+ab/2 +c + ((a+b+ab/2)c)/2= 



a*(b*c) = a*(b+c+bc/2) = 
a+(b+c+bc/2)+(a((b+c+bc/2))/2 


comparing... 
(a+b+ab/2 +c + ((a+b+ab/2)c)/2) - 
(a+(b+c+bc/2)+(a((b+c+bc/2))/2) 
which is 0 

the operation is associative 

:)