Difficulty: Hard

Average Score: 25%

Which of the following properties of operations is used when showing why 15 + 9 + 12 equals 9 + 12 + 15?

Rationale

Commutative property of addition

The commutative property of addition states that the order in which numbers are added does not affect the sum. In the expression 15 + 9 + 12, reordering the numbers to 9 + 12 + 15 demonstrates this property, confirming that both arrangements yield the same total.

A (Commutative property of addition) CORRECT

This property explicitly allows the numbers to be rearranged without changing the outcome of the addition. In this case, swapping the order of 15 and 9, while keeping 12 in the middle, illustrates that addition is independent of order, validating the equation 15 + 9 + 12 = 9 + 12 + 15.

B (Distributive property of multiplication over addition) YOUR ANSWER

The distributive property involves multiplying a single term by each term within a parenthesis, such as a(b + c) = ab + ac. This property does not apply to the rearrangement of addition terms and therefore does not explain why 15 + 9 + 12 equals 9 + 12 + 15.

C (Additive inverse property) YOUR ANSWER

The additive inverse property states that for any number, there exists another number that, when added, results in zero (e.g., a + (-a) = 0). This property is unrelated to the order of addition and does not pertain to the rearrangement of the numbers in the equation provided.

D (Additive identity property of 0) YOUR ANSWER

The additive identity property asserts that adding zero to any number does not change its value (e.g., a + 0 = a). While this property is fundamental to addition, it does not address the rearrangement of numbers in the expression and thus is not relevant to the question.

Conclusion

The commutative property of addition is the key principle that supports the reordering of terms in an addition expression. In the case of 15 + 9 + 12 and 9 + 12 + 15, this property illustrates that the sum remains unchanged regardless of the order of the addends. Other properties mentioned do not apply to this specific scenario and therefore do not explain the equality presented in the question.

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