How to re-arrange formulas for Maths GCSE - Part 2 |

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Hi. I'm Hannah from Love Learning Tutors. I am here with some Maths tutorials as part of Love Learning Tutorials. And today we're looking at rearranging equations. So this is the second in my three part series, if that's what I want to call it.

This is all focusing on x being the denominator. So what to do in this situation. If you feel like I'm skipping some stuff, and you want to go over some basics, please go back to the first video where I really go over those, and explain how to do this. And you can revisit this, and be like, hey I feel more confident now.

If you've mastered this, please check out the next video as well, they've got the most complicated examples that are available out there. But this is all really important for your GCSE, and it will come up in several other subjects, like Chemistry and Physics.


a/x = b

Okay, so let's have a look. We wanna get this x. By making it subject we wanna get it so that where we have b alone, we want get x to be there. So this is all to do with relationships of opposites.
It's not very useful to have x at the bottom of the denominator here. We can't really get rid of it that easily either. I mean, there are ways, but it’s a little longwinded. I think the easiest way to not make mistakes is to do it this way.

x x a/x = x x b

So we're going to times both sides by x. Now the reason why we do both sides is because there's an equal sign here, which means that both sides need to stay equal to each other. So what we do on one side, we do to the other. 

a = xb

By doing this, x divided by x will cancel out to make 1. And now we have a is equal to b x. There's a little times here.
From here, we're very close to the end now. So we have x on the top, which is a lot more useful. But it's tied in with this b. It's multiplied with this b. So in order to remove this b, we want to do the opposite of the multiplication, which is to divide.

a/b = xb / b

So we're going to divide both sides ... I'll just do a little division here ... by b. So by doing that, we have a over b, or a divided by b depending on how you wan to say it. b divided by b is gonna give you 1. We don't tend to right 1x, we just write x. But if you wrote 1x there, it's not wrong. But we just don't need to do it, usually.


(a + b)/x = c

Number two. So we're going to start off with exactly the same step. It's not useful to have this x at the bottom right now, so we're going to multiply both sides by x, so these are going to cancel out. We're going to end up with a plus b is equal to c times x.

a + b = cx

Okay, so we're almost there. It's very similar to this actually. It's just got an extra b hanging in there. An extra letter hanging in here. But actually the way we're working with it is exactly the same. 
So right now this c is in the way. We want this x alone.

(a + b)/c = cx/c

(a + b)/c = x

They're multiplied together, so we're going to divide the c away from both sides. So we're going to end up with a plus b over c is equal to x. Yeah. Oh, I forgot to use my red pen. I'm really big on colors, so I got really excited and bought those different colors. 

Yeah, I think that anything that makes studying more exciting for you is worth doing. But apparently, if you use more than three colors, four colors, it's not constructive anymore. It doesn't actually help your learning any more. It becomes a bit of a distraction. I'm totally guilty of that. But yeah, that's the psychological research. 


v/x + s = t

So three, here we go. We have x here, but in this case, so this isn't a times/divide situation, so we can't quite touch that yet. But we have this plus s which is much easier to get rid of. So, we're going to subtract s from both sides. So we have v over x is equal to t minus s.

v/x = t - s

From here, we have a similar situation to all these other guys. So we have x as a denominator by itself, as in like, it's not with the s. So this means you want to times both sides by x, because we want the x up on the top, because it's more useful to us that way. So, I'm just gonna put this in brackets right now.

v/x = (t-s)

x x v/x = (t-s)x

So here's t minus s. And we've multiplied it by x. And this just means that both t and minus s are both multiplied by this x. More that me explaining the brackets, I want to get rid of this very, very soon, cos I'm just gonna leave it like that.

v / (t-s) = x

So the x is so close to being alone. And we've got this multiplication relationship with what's inside the brackets. So, it's times, so we need to do the opposite. And we can get rid of this whole chunk in one go, as it's in the brackets. Which is very convenient.

We're dividing both sides by t minus x. So, this will cancel out to make one.

We've made the subject of all three, despite it starting out as a denominator.

I hope that was very, very helpful for you. Please comment below if there are any questions you have with x as a denominator that you've not quite been able to solve. And check out our next video, which is gonna be the more complicated ones. 

If you've done all three of those, and you're happy and quite confident with those, I see no reason why you wouldn't get full marks in rearranging changing subject/question in your exam paper. 

Thank you so much for watching. Please like, share, subscribe. Bye.