Algebra, ring question with even integers

[jasonfarley89]

We have E the set of even integers with ordinary addition Define new multiplication * on E defined as

a*b = ab/2 where on the right hand side of the equation is just normal multiplication.

I am just a bit confused i am trying to show Associative multiplication meaning i have to show

(a*b)*c = a*(b*c)

when i do (a*b)*c am i supposed to get (ab/2)(c/2) ?? i feel like i am just doing something really stupid here

Can someone explain? Its binary operation so it can only take two elements at a time right?

also i am bit confused with distributive law,

so a*(b+c) = a(b+c)/2? i want to be equal to (ab)*(ac) = ab(ac)/2 right?

Can someone help please

 

[jasonfarley89]

should it be that (a*b)*c = (ab/2) *c = ab/2(c/2) so i have ab(c/2)/2 = (abc/2)/2 = abc/4? that correct?

 

[ystael]

Yes, that's correct, although I might parenthesize it a little differently: $$(a * b) * c = (ab/2) * c = ((ab/2)c)/2 = abc/4$$.

For the distributive law, you want $$a * (b + c) = a * b + a * c$$, not $$a * (b + c) = ab * ac$$.