Question

Explain why the commutative and associative properties don't hold true for subtraction and division but the identity properties do

Answer 1

6 -9 is a negative number (-3)  but 9-6 is a positive number (3)

Therefore 6-9 ≠ 9-6 and subtraction is not comutative

Same for division:

6 ÷ 3= 2   but 3 ÷ 6 = 1/2 (the inverse of 2)

so 6÷3≠ 3÷6 and division is not commutative either

Now lets look at the associative properties

(4 - 6 ) -3 = -5   but  4 -( 6-3) = 1   so associative property does not give the same result.  Subtraction is not associative  

(35 ÷ 7) ÷5 = 1   but  35 ÷ (7÷5) = 35 ÷ 1 2/5 and is not the same answer.
Division is not associative.

7- 0 is still 7 so the identity property works for subtraction just as it does for adding
7÷1 is still 7 so the identity property works for division just as it does for multplication
Note well that the identity property in + and - is 0
but in x and ÷ it is 1