FTCE Professional Education Practice Exam

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What does the commutative property state regarding addition?

You can regroup the terms as you like
The order of the terms or factors can be changed
Addition is only defined for real numbers
Zero is the additive identity

The correct answer is: The order of the terms or factors can be changed

The commutative property regarding addition states that the order of the terms can be changed without affecting the sum. This means that for any two numbers, the sum will remain the same regardless of the sequence in which they are added. For instance, if you add 2 and 3, you will get the same result (5) whether you calculate it as 2 + 3 or 3 + 2. This property is fundamental in mathematics as it simplifies calculations and allows for flexibility in problem-solving. In contrast, regrouping terms pertains to the associative property, which involves how numbers are grouped in addition, rather than the order in which they are placed. The exclusive definition of addition only for real numbers restricts the broader application of the commutative property, which is applicable to any number system that includes addition. Lastly, while zero as the additive identity is an important concept in mathematics, it does not relate specifically to the order of additions, as stated by the commutative property.