How to re-arrange formulas for Maths GCSE - Part 1 | The basics

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Video Transcript:

Hi. I'm Hannah from Love Learning Tutors, and today, we're doing some maths tutorials as part of Love Learning Tutorials. 

So, first here I'd like to look at some rearranging equations. Sometimes they call it changing subject. Sometimes I notice students having troubles with this until quite close to their GCSE exams, so it's definitely worth making sure you've mastered, as a foundation for the rest of all your other maths bits and pieces that you need to do.

These are three examples.

I'll be doing another video with X on the bottom of the fraction, so you can see that. And then slightly more complicated ones after. So once you've mastered this, please go and check them out, too.

To begin with, the name of the game is we want to get X by itself. The way that you need to think about it is in terms of opposite relations. So where something's added, you want to subtract it to move it. Or if something's times-ed, you want to divide it to remove it, and vice versa.

ax + b = c

1)
So with this first example here, this X is kind of unapproachable right now. There's a secret little times sign between a and x. We don't tend to write it. We just put the two letters together, but although it’s not written, they do have a multiplication relationship to each other. So at the moment x is kind of locked in. The first things that you want to get rid of are things that are added or subtracted on either side. 

So in this example, we have a plus b, so the opposite of plus b is minus b. In order to both sides are always the same, what we do on one side, we must do to the other. So if we subtract the b from this side, we have to subtract the b from this side. This makes the next line…

ax = c-b

The bs cancel each other out. And then we have c minus b here.

We're actually very close now. So as we discussed before, this is a times. They have a times relationship. So what is the opposite? It's divide. We want to keep the x on the left hand side, so it's the a that we're dividing out of the situation. We divide both sides by a.

ax/a = b/a

So a divided by a will give you one. Now, we don't tend to have ones in front of our letters. If it was 2x for example, it would say 2x. But just for 1x, we just tend to write x just by itself.

x = (c-b)/a

Is equal to c-b, what we had before. And it's all over that a. So that's our first one.

2)
Number two!

d=(x-b)/c

Now, this one's locked into a fraction. So at the moment, we can't really get to it, because it's all tied up. We need to remove this c first. It's clearly in the way. When what we want to remove is at the bottom of a fraction, it means it's divided. x minus b is divided by this c. Which means the way to remove the c is to do the opposite, so we want to multiply both sides by c. 

So c divided by c will just give you 1. Now we have have…

c x d = x-b

We don't really need this times here. We just write cd. Or you can keep the times sign there. That's completely up to you. It's inferred even if you don’t write the sign.

It’s now minus b we that we have next to the x, so we have to add b to both sides.

cd+b= x

So in essence, we have cd + b is equal to these two canceled out, so that makes our x ... So let's give that a tick. So we have X is the subject, which was the goal. Okay.

3)
So last one! number three.

a(x+c) = e

This one involves a little bit more. But not really too much. This is the first example we've seen with brackets, isn't it? So in essence, when we have a letter next to a bracket, do you know what relationship it has with the bracket? Similar to how we have two letters together it had a secret times or an invisible times, this is exactly the same here. So we can't get to this x yet because it's locked into this bracket situation.

The easiest thing to remove is this a. So what's the opposite of times-ing a is dividing by a. So a divided by will just make one. So then we have…

x + c = e/a

You might have noticed that I've removed the brackets now, but as it's just how it is inside the brackets, we don't need them there anymore. So super simple. Almost at the end. So we have a plus c. So the way to get x by itself is to remove this extra plus c by taking c away from both sides. Pow, pow. 

So we get…

x = e/a - c

x is equal to e over a minus c. Amazing. 

Okay. So those are the first three examples. If you want to see what happens when we have X at the bottom which throws many people off, please check out our next video. Please like, subscribe, share with your friends if you found it useful. Let us know what you think. These are all built around you and what you guys want to know.

Thank you so much for watching. Bye!