The statement a+b = b+a illustrates which property?

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Study for the GACE Elementary Education II Test. Prep with flashcards and multiple-choice questions, each with hints and explanations. Get ready for your exam!

Multiple Choice

The statement a+b = b+a illustrates which property?

Explanation:
The statement shows that order doesn’t matter in addition. For any numbers a and b, swapping their positions gives the same result: a + b equals b + a. For example, 4 + 9 equals 9 + 4, both 13. This property—reordering the addends without changing the sum—describes the commutative property of addition. The other ideas refer to different rules: distributive would involve multiplying over a sum (a(b + c) = ab + ac); transitive is about chains of equality (if a = b and b = c, then a = c); and cardinality relates to the size of a set.

The statement shows that order doesn’t matter in addition. For any numbers a and b, swapping their positions gives the same result: a + b equals b + a. For example, 4 + 9 equals 9 + 4, both 13. This property—reordering the addends without changing the sum—describes the commutative property of addition. The other ideas refer to different rules: distributive would involve multiplying over a sum (a(b + c) = ab + ac); transitive is about chains of equality (if a = b and b = c, then a = c); and cardinality relates to the size of a set.

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