What property allows the order of numbers to be swapped in addition or multiplication without changing the result?

The property that allows the order of numbers to be swapped in addition or multiplication without changing the result is known as the Commutative Property. This property states that for any two numbers, the result of their addition or multiplication remains the same regardless of the order in which they are arranged.

For instance, when adding two numbers, such as 3 and 5, both 3 + 5 and 5 + 3 equal 8. Similarly, in multiplication, both 4 × 2 and 2 × 4 equal 8. This interchangeability emphasizes that the sequences of the numbers do not impact the outcome when performing these operations.

In contrast, the Distributive Property pertains to the way numbers are multiplied over addition or subtraction, the Associative Property relates to grouping numbers in addition or multiplication, and the Additive Identity refers to the concept that adding zero to any number does not change its value. Understanding these properties is essential for grasping fundamental arithmetic operations and their applications.