Question 66

15 + 9 + 12 equals 9 + 12 + 15 due to the commutative property of addition.

The commutative property of addition states that changing the order of addends does not change the sum. Therefore, rearranging 15 + 9 + 12 to 9 + 12 + 15 maintains the equality of the expression.

A) Commutative property of addition

This option correctly identifies the property that allows the rearrangement of the addends. According to the commutative property, the order in which numbers are added can be changed without affecting the total, making this the correct choice.

B) Distributive property of multiplication over addition

This option is incorrect because the distributive property pertains to multiplication distributing over addition (e.g., a(b + c) = ab + ac) and does not apply to the rearrangement of terms in addition.

C) Additive inverse property

This option is incorrect as the additive inverse property refers to the concept that a number plus its inverse (e.g., a + (-a) = 0) equals zero. It does not involve changing the order of addition.

D) Additive identity property of 0

This option is incorrect because the additive identity property states that adding zero to a number does not change its value (e.g., a + 0 = a). It does not relate to the rearrangement of terms in addition.

Conclusion

The commutative property of addition is the key principle that explains why 15 + 9 + 12 equals 9 + 12 + 15, as it allows the addends to be rearranged freely. All other options describe different mathematical properties that do not apply to the situation presented in the question. Thus, option A is the only correct choice.