Which property is used when rearranging terms in an expression while keeping the result the same?

The commutative property is used when rearranging terms in an expression while keeping the result the same. This property states that changing the order of the numbers involved in addition or multiplication does not affect the sum or the product. For example, in addition, ( a + b = b + a ) and in multiplication, ( a \times b = b \times a ). This means that you can rearrange the terms without changing the outcome, which is exactly what is being described in the question.

The other properties serve different functions: the associative property involves regrouping terms, the distributive property combines multiplication with addition or subtraction, while the additive property relates specifically to the identity of zero in addition. Each of these properties has its own unique application and is not about merely rearranging terms.