 In this video, I want to talk a little bit about rearranging equations. And this is an algebra issue, but it's one that sometimes causes students some issues. And as an example, I'm just going to go ahead and take a look at a couple of the equations that we use in one of the early chapters in my physics class. So here's one of the equations we'll work on rearranging. And then my next equation, and we'll work on rearranging that one. Now when we work with doing algebra on equations, we have to keep in mind the order of operations. And different teachers teach it different ways, but you have to do parentheses, exponents, multiplication and division go together, and then addition and subtraction. Some people call this PEMDAs or other such things. So what that means is that this quantity in parentheses over here, this Vi plus Vf, are closely bound together, more closely bound together than the multiplication in front of and behind it. And over here in this equation, because there aren't parentheses, this multiplication is more tightly bound together than this addition. So keeping those rules of operation in mind is really going to help you as you're working through. So let's say I was going to rearrange this equation and I wanted to solve for the Vi. Well it's right now bound to the plus Vf inside the parentheses, but more loosely to the multiplication and division, because multiplying by one half is like dividing by two. So I could go ahead and multiply both sides by two, and that would leave me with Vi plus Vft, but now the two has moved over to the other side. But it's multiplied since it was originally divided. And then I can divide both sides by the time, and when I do that it cancels out on the right hand side. Now I didn't show the actual multiplication and division here, although I could have. I could have said here that you divide both sides by time, time then cancels, and that's how I get my equation below. Once I've done that, now I'm down to something which is just in parentheses. So if I was going to now work with this, because there's nothing else that can come outside of the parentheses, and I can now subtract the Vf on both sides, which would leave me with the two delta x over t minus Vf equals Vi. And I've got my full equation if I'm trying to solve for Vi. I could do the same sort of thing over here on this equation. And again, let's say I'm going to solve for Vi. Well, in this particular case, because I have the At, which are bound together, but they're added, what I can do is subtract off that At on both sides. And I'm left with Vf minus At equals Vi. I never had to separate those two because those weren't the things that I'm solving for. So let's look at these same two equations now. Look at a different example. Let's say in both of these equations, I wanted to solve for the time. Now I'm going to go ahead and recopy them just so we can keep track a little easier. Here I've got my delta x is 1 half Vi plus Vft. And here I had my Vf equals Vi plus At. And now I want to rearrange these equations as if I was solving for the time. So again, we want to go through and do some operations. Now in this case, again, I've got a divide by 2 so I can multiply both sides by 2, leaving me with 2 delta x equals Vi plus Vft. And then because these are bound in parentheses, I can actually go through and divide by the whole thing still held in parentheses. And that's going to leave me with 2 delta x over Vi plus Vf is equal to t. Just scrolling up so you can see better. Over here on this side, well, again, the At are bound together, but the Vi is more loosely connected. So I can go ahead and subtract that off first, which would leave me with Vf minus Vi equals At. Now we can deal with the division because they were originally multiplied. The inverse operation would be the divide. And it divides the entire quantity there. So I'm left with Vf minus Vi. And you might want to put some parentheses around that now just to clarify. All divided by A equals t. So as you're working through doing algebra rearrangements, remember that the order of operations matters. And we're kind of working backwards through things and figuring out which things are more closely connected and which ones are more loosely connected. So that we can do the inverse operations to be able to rearrange things. If you have any more questions on rearranging equations and you're one of my students, go ahead and contact me and I'll help you walk through some of the steps.