Final answer:
The commutative property does not apply to rational number subtraction because changing the order affects the result, characterized by the anticommutative property. Likewise, the associative property does not apply because regrouping the terms affects the outcome.
Step-by-step explanation:
The commutative property of rational number subtraction does not apply. In mathematics, the commutative property refers to the ability to change the order of the numbers involved in an operation without changing the result. This is true for addition (e.g., A + B = B + A), but not for subtraction, because changing the order of the numbers does change the result (e.g., A - B ≠ B - A). Therefore, subtraction is said to have an anticommutative property, meaning that a change in the order of operation introduces the minus sign.
The associative property also does not hold for subtraction. The associative property pertains to how terms are grouped and suggests that operations can be performed regardless of how the numbers are grouped (e.g., (A + B) + C = A + (B + C) for addition). However, with subtraction, regrouping terms can lead to different results, and thus the associative property cannot be applied to subtraction in the same way it applies to addition. For instance, (A - B) - C is not necessarily the same as A - (B - C).