In Exercises 75–84, state the name of the property illustrated. 7...

Question

In Exercises 75–84, state the name of the property illustrated. 7⋅(11⋅8)=(11⋅8)⋅7

Accepted Answer

Hello. Everyone in this video we're going to be identifying the mathematical property being observed in the equation 11 times parentheses one times seven is equal to parentheses one times seven times 11. So in this equation you can see that there's sort of two components. We have the 11 that appears on both sides and we have the one times seven that also appears on both sides. So in order to try and highlight the differences between the two, I'm going to assign variables to try and see what is changing between the left hand side and the right hand side. So I'm gonna say a is equal to 11 and B is equal to parentheses one time seven. So now I can rewrite the equation as A times B is equal to B times A. So 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 multiply so because there's nothing changing with the parentheses. And the only thing that is changing is the order in which we multiply. And when we change the order of multiplication, the solution stays the same. So the left hand side and the right hand side are equal to each other. It is known as the community of property. And specifically because it's multiplication, it would be the community of property of multiplication. And recall that you can't have the communicative property for division because if we change the division order. For example if we had a divided by B. This is not the same as B divided by A. So the community of property can only exist for multiplication or addition, and when the order of operation changes, but we get the same solution, so hopefully this helped.