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Which equation shows the associative property of addition?
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First, let’s address what the associative property of addition is.
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The associative property of addition tells us that we can regroup addends without changing the sum.
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The word “regroup” here deals with parentheses or brackets.
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Let’s look at our answer choices.
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Choice a) is adding the negative of an 𝑥-value plus the positive of an 𝑥-value.
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It does not represent a regrouping.
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Choice b) is a regrouping, but it’s dealing with multiplication.
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And we’re looking for a regrouping of addition.
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Answer choice c) changes the order that we’re adding but does not group anything differently.
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Choice d) is a distribution of the multiplication, which leaves us with choice e).
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On the left side, 𝑥 plus three is grouped together.
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And on the right side, two plus 𝑥 is grouped together.
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This regrouping will not affect the outcome.
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These two sentences are equal and they show the associative property of addition.