In the solution of four times 𝑥 minus three equals 24, consider these steps. In going from the second equation to the third equation, the fact that one-fourth times four equals one is used. What other property of numbers is used in this step?
We wanna know what is happening to get us from here to here. What properties are we using that allow us to simplify and reduce these steps? Let’s take a closer look at what is happening. There is multiplication happening here. We’re multiplying one-fourth times four times 𝑥 minus three.
Now because these are in parentheses, we would typically do this part of the equation first. But because both of these steps are multiplication, we can actually change the order. We can multiply one-fourth times four first. And because one-fourth times four equals one, this is a slightly simpler way to reduce this problem. The associative property allows us to do this — allows us to change the grouping. So what we’ve done here as we change the way the grouping for multiplication worked. And that is all from the associative property.