Kaplan Nursing Entrance Practice Exam

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What is the primary mathematical principle demonstrated by the equation 1 + 3 = 3 + 1?

The distributive property
The associative property
The commutative property
The identity property

The correct answer is: The commutative property

The equation 1 + 3 = 3 + 1 demonstrates the commutative property, which states that the order in which two numbers are added does not affect the sum. In this case, whether you add 1 to 3 or add 3 to 1, the result remains the same: both yield a sum of 4. This property applies to addition and multiplication but does not apply to subtraction or division. Understanding the commutative property is essential in mathematics, as it allows for flexibility in computations and simplifies problem-solving processes. The other properties listed—distributive, associative, and identity—each serve different functions in mathematics: the distributive property relates to how multiplication interacts with addition, the associative property pertains to how numbers are grouped in addition or multiplication, and the identity property refers to how certain numbers (like 0 and 1) act as 'identities' in addition or multiplication. Therefore, the correct identification of the commutative property in this context highlights the fundamental nature of operations within arithmetic.