Which property ensures that the same result is produced regardless of the order of numbers being added or multiplied?

The property that ensures the same result when the order of numbers being added or multiplied is changed is known as the commutative property. This property applies to both addition and multiplication, allowing us to rearrange the numbers freely without affecting the outcome. For example, when adding the numbers 3 and 5, the result is the same regardless of the order: 3 + 5 equals 8 and 5 + 3 also equals 8. Similarly, for multiplication, 4 multiplied by 6 yields the same result as 6 multiplied by 4, both equaling 24.

This property is fundamental in arithmetic and algebra, allowing for flexibility in calculations and simplifying expressions. Understanding and applying the commutative property is essential for students as they progress in mathematics.