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+(−4)=(−4)+6

Accepted Answer

Hello, everyone in this video, we'll be trying to identify the mathematical property being observed in the equation plus 21 is equal to 21 plus 12. So in order to try to highlight the differences, I'm going to re assign variables to the components. Where you can see that we have a 12 on the left hand side and the right hand side. And we have a 21 on the left hand side and the right hand side. So I'm gonna say A is equal to 12 And B is equal to 21. And when I do that I can rewrite the equation as a plus B is equal to B plus A. And you can see that not much is changing between the left hand side and the right hand side except for the order in which we're adding the variables. So one of the only things that is changing is the order in which be addition occurs. And both the left hand side and the right hand side have the same solution where the left hand side is equal to 33 and the right hand side is equal to 33. So when the order of addition changes, but the solution remains the same. That is known as the community of property. And remember that the community of property only exists for addition or multiplication because if we try to do A minus B is equal to Yeah, B minus a. You can see that we won't get the same value because we would have 12 minus 21 is equal to 21 minus 12. And and the left hand side we would get a negative value. And on the right hand side we would get a positive value. So this cannot be so the community property can only exist for addition or multiplication. And in this case we're observing the community property of addition, since we're changing the order of addition, but getting the same solution. But hopefully this video helped see you next time.