Which property states that numbers can be moved around in an equation without changing the result?

The property that allows numbers to be rearranged in an equation without affecting the outcome is the commutative property. This property applies to both addition and multiplication, enabling the order of the numbers to change while the result remains the same. For example, in addition, (3 + 5) gives the same result as (5 + 3), and in multiplication, (4 \times 2) is equal to (2 \times 4). This flexibility in the arrangement of numbers is a fundamental concept in arithmetic that allows for various methods of calculation and problem-solving.

In contrast, the associative property pertains to how numbers are grouped in an expression, which can alter the positioning of parentheses but not the order of the numbers themselves. The additive property generally refers to the concept of adding zero to a number, while the distributive property involves distributing a multiplied term across terms within parentheses, demonstrating how multiplication interacts with addition or subtraction. These distinctions clarify why the commutative property is specifically the one that addresses the rearrangement of numbers in equations while maintaining the same result.