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Question Video: Identifying the Associative Property with Rational Numbers Mathematics • 7th Grade

Which equation shows the associative property of addition? [A] (1/2) + (−1/2) = 0 [B] (1/2) + (2/3) = (2/3) + (1/2) [C] (1/2) + (2/3) = 7/6 [D] ((1/2) + (2/3)) + (3/4) = (1/2) + ((2/3) + (3/4)) [E] (2/3) + 0 = 2/3

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Video Transcript

Which equation shows the associative property of addition? Is it (A) a half plus negative a half equals zero? (B) One-half plus two-thirds equals two-thirds plus one-half. Is it (C) one-half plus two-thirds equals seven-sixths? (D) One-half plus two-thirds plus three-quarters equals one-half plus two-thirds plus three-quarters. Or (E) two-thirds plus zero equals two-thirds.

Remember, the associative property of addition says that the sum of three or more numbers remains the same regardless of how the numbers are grouped. So, we’re going to go through each of our equations and identify which of these satisfies the associative property. We’re going to disregard (A) immediately. (A), in fact, is showing us an example of the additive inverse. The additive inverse of one-half is negative one-half because the result is zero when we add them. And what about (B)? Well, no, the associative property does tell us we can perform the addition in any order but that there are going to be three or more numbers, and it’s regardless of how those three or more numbers are grouped. So (B) does not show the associative property. (C) just gives us an equation. It tells us that a half plus two-thirds equals seven-sixths, and so it’s not (C).

So, what about (D)? We do indeed have three numbers on each side of our equation, and they’re grouped differently on both sides. Otherwise though, the numbers remain unchanged. So, yes, (D) does show the associative property of addition. If we perform a half plus two-thirds first and then add three-quarters, that’s the same as adding a half to the result of two-thirds plus three-quarters. And so the answer is (D). (D) shows the associative property of addition. We can see quite clearly it’s not (E). That’s just showing us that when we add zero to a number, it remains unchanged.

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