Question 66

The commutative property of addition is used to show that 15 + 9 + 12 equals 9 + 12 + 15.

The commutative property of addition states that the order in which two numbers are added does not change the sum. Therefore, rearranging the numbers in the expression does not affect the total.

A) Commutative property of addition

This option is correct because it directly refers to the principle that allows for the reordering of addends. In the expression 15 + 9 + 12, the addition can be rearranged to 9 + 12 + 15 without changing the result, demonstrating the commutative property.

B) Distributive property of multiplication over addition

This option is incorrect as it pertains to the distribution of multiplication over addition, not addition itself. The distributive property is used when multiplying a number by a sum, such as a(b + c) = ab + ac, which is not relevant to the question about addition.

C) Additive inverse property

This option is incorrect because the additive inverse property involves the concept that a number plus its opposite equals zero (e.g., a + (-a) = 0). It does not apply to the reordering of terms in addition.

D) Additive identity property of 0

This option is also incorrect, as the additive identity property refers to the fact that adding zero to a number does not change its value (e.g., a + 0 = a). It does not relate to the rearrangement of addends in an addition expression.

Conclusion

The commutative property of addition is the principle that justifies the rearrangement of numbers in an addition expression without altering the sum. Options B, C, and D do not pertain to the concept of changing the order of addends and therefore are not applicable to this question.