Question

Why the commutative and associative properties don't hold true for subtraction and division

Answer 1

The commutative and associative properties do not apply to both subtraction and division because once you move around your variables, you will produce different results, whereas in addition and multiplication, any change in position of numbers won't affect the result. The identity properties apply to them because once you add, subtract, multiply, or divide a certain number from any other number, you produce the same result, or, in other words, keep the number's "identity".