Video: Associative Property of Addition

Which equation shows the associative property of addition? [A] (−𝑥) + 𝑥 = 0 [B] 2(𝑥3) = (2𝑥)3 [c] 2 + 𝑥 = 𝑥 + 2 [D] 2(𝑥 + 3) = 2𝑥 + 6 [E] 2 + (𝑥 + 3) = (2 + 𝑥) + 3

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Video Transcript

Which equation shows the associative property of addition?

First, let’s address what the associative property of addition is. The associative property of addition tells us that we can regroup addends without changing the sum. The word “regroup” here deals with parentheses or brackets.

Let’s look at our answer choices.

Choice a) is adding the negative of an 𝑥-value plus the positive of an 𝑥-value. It does not represent a regrouping.

Choice b) is a regrouping, but it’s dealing with multiplication. And we’re looking for a regrouping of addition.

Answer choice c) changes the order that we’re adding but does not group anything differently.

Choice d) is a distribution of the multiplication, which leaves us with choice e).

On the left side, 𝑥 plus three is grouped together. And on the right side, two plus 𝑥 is grouped together. This regrouping will not affect the outcome.

These two sentences are equal and they show the associative property of addition.

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