In Exercises 75–84, state the name of the property illustrated. 6...

Question

In Exercises 75–84, state the name of the property illustrated. 6+(2+7)=(6+2)+7

Accepted Answer

Hello Today we're going to be identifying what property is shown in the given equation. So what we are given is one. Plus the quantity 14 plus nine is equal to the quantity one plus 14 plus nine. Now, quickly we can identify that this is the associative property because the associative property states that if we have a plus the quantity B plus C. That is going to equal to the quantity A plus B plus C. Essentially what this is saying is if we are adding the sum of three numbers, no matter how we group these numbers, both sides of the equation is going to be the same here. One is a. B is 14 and C is nine, so it's clearly representing the associative property. But we also need to verify that both sides of this equation are going to equal to each other. So let's go ahead and work that out real quick On the left hand side, 14 plus nine is going to give us 23 so we have one plus 23 is equal to one plus 14, which is going to give us 15 plus nine. On the left hand side, 23 plus one is going to give us 24. And on the right hand side, 15 plus nine is going to give us 24. So 24 is equal to 24 is a true statement. So we are representing the associative property because we are grouping up the same three numbers but differently. And no matter how we group up these three numbers, both sides of the equation are equal to each other, so the answer to this problem is going to be D. So I hope this video helps you in understanding how to identify the associative property for addition, and I'll go ahead and see you all in the next video.

In Exercises 75–84, state the name of the property illustrated. 6+(2+7)=(6+2)+7

Key Concepts

Associative Property of Addition

Commutative Property of Addition

Properties of Operations

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