Narrator: A number of hints have been introduced in Chapter 3 to help you when rearranging equations. This video sequence illustrates the use of these hints in rearranging five equations of increasing complexity, and you will soon realise that the principles involved remain the same, no matter how complex the equation appears to be.

You may find it helpful to view the sequence more than once, and to pause from time to time to check your understanding. You may like to stop part-way through, at the time indicated, to try some questions for yourself .

We'll start with a very simple problem. Alison has to rearrange an equation and Shelagh, her tutor, is helping her.

Alison: So, er, I am asked to rearrange the equation in terms of f but I don't even know what the symbols mean. [Laughter].

Shelagh: Well, don't worry about it. Um, E is the energy of a photon, denoted by the subscript, so we'll call that E photon.

Alison: Right. Okay.

Shelagh: And h is something called Plank's constant and f is the frequency of the light.

Alison: Right.

Shelagh: But don't get hung up about the symbols for the moment.

Alison: Right.

Shelagh: Um, let's just work with the equation.

Alison: Okay.

Shelagh: So what does h f actually mean?

Alison: Um, h multiplied by f.

Shelagh: Yeah.

Alison: So, so I could, I could write it like that.

Shelagh: You could.

Alison: Okay.

Shelagh: You can write it either way. We would normally miss out the multiplication sign but, if you are more comfortable putting it in, that's fine as well.

Alison: Okay.

Shelagh: So what's the subject of the equation at the moment?

Alison: E photon because it, it, because it's on the left and it's by itself.

Shelagh: Right. And what do we want to make the subject?

Alison: f.

Shelagh: Okay. So let's just write that there so we know where we are heading.

Alison: Yeah.

Shelagh: So a really good way to start would be to try and at least get f on the left-hand side where it belongs as the subject.

Alison: Yeah.

Shelagh: How could you do that?

Alison: Um, could you just write the equation that way round?

Shelagh: Yes, because it's the reverse.

Alison: It's the same isn't it, yeah.

Shelagh: It's exactly the same, yes. So at least now you've got f on the left where you want it.

Alison: Yeah.

Shelagh: But you've still got it multiplied by this h.

Alison: Yeah.

Shelagh: So how could you get rid of the h?

Alison: Divide by h.

Shelagh: Yes, divide what by h?

Alison: Divide both sides of the equation by h.

Shelagh: Indeed, because you are always trying to keep a balance. Whatever you do to one side of the equation, you must do to the other side and then the balance is preserved.

Alison: Yeah. Yeah.

Shelagh: So why don't you try that?

Alison: Okay, so I've divided this side by h and then do E photon over h and then ...

Shelagh: Yes, um ...

Alison: ... the hs on this side cancel so that leaves me with f equals E photon over h.

Shelagh: And you've done it.

Alison: And I've done it. I've made f the subject.

Shelagh: Fantastic.

Narrator: Let's just look again at the hints Alison used in rearranging this equation. She started off by reversing the equation. This enabled her to get the f , the term that she was trying to make the subject, into place on the left-hand side. After that she was applying the important rule that whatever you do to one side of an equation you must also do to the other side. But Alison had to decide WHAT to do to both sides of the equation. In this case, the term she wanted, the f, was multiplied by h - so she divided both sides by h.