Properties Math Problems!!! PLZ HELP!!!

1. Justify the statement, "Division is not commutative."

Commutative would mean that a / b  = b / a

But......  4/3  ≠  3/4   ....so.........division is not commutative

2. Show that the set of non-zero rational numbers is closed under division.

We want to show that dividing a non-zero rational by a non-zero rational produces another non-zero rational

Let the first rational = a/b and the second =  c/d     where a,b,c,d   are non-zero integers

Then.....

a/b ÷  c/d  =

[ab] * [d/c]  =

[ad] / [ bc]         but, since a,d are non-zero integers, so is their product......and the same with b, c

Thus.....dividing a non-zero rational by a no-zero rational produces another non-zero rational