What property states that changing the grouping of numbers will not change their value?

The Associative Property states that changing the grouping of numbers in an operation does not affect the result. This property applies to both addition and multiplication. For example, when adding numbers, if you have (a + b) + c, it is equal to a + (b + c). The way the numbers are grouped does not change the sum. Similarly, for multiplication, (ab)c is equal to a(bc). This property is fundamental in arithmetic, ensuring that regardless of how numbers are paired or grouped, the outcome remains consistent.

The Distributive Property, on the other hand, involves distributing a multiplication over addition or subtraction, so it is not about grouping. The Commutative Property refers to changing the order of the numbers, which affects their positioning but not their grouping. The Identity Property involves the identity element of an operation (like adding zero or multiplying by one) and is also unrelated to grouping. Thus, the Associative Property uniquely encapsulates the idea that regrouping numbers doesn't change their total value.