Rearranging equations, just can't seem to get it!

Hey for some inexplicable reason I can never grasp the 'rules' when it comes to rearranging equations. I can rearrange equations fine until it comes to equations with powers or fractions in. They everything just seems to go into meltdown! Are there some simple rules as to what you can and can't cancel, when you multiply by the denominator to get rid of the fraction etc. Also simplifying equations what are the rules for cancelling between top and bottom? I'm running into problems, never did maths A level and its been a looooong time since GCSE maths so I think I've forgotten rather a lot! Any help much appreciated, even if you go all the way back to the beginning it is probably a good thing :smile:

(edited 12 years ago)

Reply 1

steve2005

This might be a good place to start.

http://www.teacherschoice.com.au/maths_library/algebra/alg_21.htm

Too simple, try here
http://www.sosmath.com/algebra/solve/solve0/solve0.html

(edited 12 years ago)

Reply 2

Mountain One

Thanks for the links, I've had a quick scan through but still confused, can i check my answer and show you my workings so you get an idea of the (probably) highly erratic thought process, sorry don't have a anything to make it easier to read!

s = ut + 1/2 at^2

trying to rearrange for a:

(x 2 to get rid of fraction)
2s = 2ut + at^2

(-2ut to get rid of it from the right)
2s - 2ut = at^2

(divide by t^2)
2s - 2ut/t^2 = a

is that correct? and is that equivalent to

a = 2(ut-s)/t^2

as far as i can work out it isn't because I have 2s-2ut rather than 2ut-2s but i'm never 100% certain about things like this.

ok then my next question is about rearranging s = ut+1/2 at^2 for t. Now reading the links above it says about collecting all of the same terms together, now when i try that i just get into a tangle and a vicious circle of multiplying and dividing things. Could you talk me through the process. Help is really appreciated!

Reply 3

steve2005

Are you required to make 'a" the subject? I would put the values you know into the original equation and then solve for the acceleration.

Reply 4

steve2005

If you are not required to make 'a' the subject then I wouldn't bother.

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Reply 5

Mountain One

thank you

sadly i'm practising rearranging equations for different terms rather than trying to solve anything. Really appreciate your help, and pretty chuffed that I managed to get it right!

Reply 6

Circadian_Rhythm

Original post by Mountain One

ok then my next question is about rearranging s = ut+1/2 at^2 for t. Now reading the links above it says about collecting all of the same terms together, now when i try that i just get into a tangle and a vicious circle of multiplying and dividing things. Could you talk me through the process. Help is really appreciated!

Post your workings for 't' and we'll see what you do :smile:

Reply 7

Mountain One

well said it was horrific...

s = ut + 1/2at^2

rearrange for t

(x 2 to get rid of fraction)
2s = 2ut +at^2

(trying to collect t together so)

2s/2u = 2t + at^2/2u

and this is where i keep hitting a wall since i've managed to get rid of the 2u from 2ut but now caused major problems elsewhere! Now i need to get rid of a and 2u from the same bit but if i multiply by 2u i just reintroduce it to t...

so then my next bright idea was this!

s - ut = 1/2 at^2

(x2 to get rid of fraction)

2s - 2ut = at^2

2s - 2ut/a = t^2

(brilliant i think starting to get somewhere but still have a t on the wrong side so + 2ut don't think you can even do that???)

2s/a = t^2 - 2ut

(/ by u)

(2s/a)/u = t^2 - 2t

(2s/a)/u = -2t^2

(then divide by -2)
((2s/a)/u)/-2 = t^2

(then sqr root the whole sorry mess to get t)

which then reads something awful like
sqr root ((2s/a)/u)/-2 = t

so yes i dont have a clue how to rearrange it is the upshot of that :smile:

Reply 8

MissBrown

You have a couple of errors in there such as the division by u.
In all honesty I would expect you to have some values to work with and rarely will you have to go through the process.
To make t the subject though just use the qudratic equation or complete the square. The former being easier.

Reply 9

Andythepiano

I tell my students who are struggling with this to use BIDMAS in reverse (SAMDIB) when rearranging and it helps in a significant fraction of cases if they were confused by other methods

Reply 10

TenOfThem

I realise that you have chosen a general equation to practice on but this is one where you would not be asked to rearrange for t because you have t and t^2 so you would have a quadratic in t

Reply 11

steve2005

Original post by TenOfThem

I realise that you have chosen a general equation to practice on but this is one where you would not be asked to rearrange for t because you have t and t^2 so you would have a quadratic in t

No. You can be required to do this and to do it you could use 'completing the square'

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(edited 12 years ago)

Reply 12

JoshW418

I'm in the same boat as the OP! :smile:

I just don't get it. It seems to be intuitive to other people and teachers to the point where they assume that the /reasons/ why they take each step don't need explaining. I can rearrange simple equations fine, but anything even remotely complicated throws me off. What I'm currently pulling my hair out over is:

10pq+9pr+10p+1=3q+6
so you get easily get rid of the +1
10pq+9pr+10p=3q+5
then on the next step, you can factor out the p, which I understand once I checked the answer but while I was attempting the question, it didn't occur to me to do that.
p(10q+9r+10)=3q+5.

I was sat at this step for ages until I caved in and looked at the answer, which apparently was only one step away, and was:

p=3q+5/10q+9r+10

.... WHAT?!?! I don't know how that leap even makes sense, let alone how I would have got there on my own. Feel like I'm hitting my head against a wall. I can't even comprehend the problem far enough to lay out exactly what I don't understand, but I suppose if I could summarise, it's that I don't understand how p(10q+9r+10) can just be broke in half and slapped on the other side of the equation - I don't see any rhyme or reason to that.

Reply 13

fmartino

Original post by JoshW418

I'm in the same boat as the OP! :smile:

You look at numbers and letters the wrong way

If it was:
p(7)=3q+5.
what would you do? Just divide 7 so:

p=3q+5/7

Now imagine
p(10+ r)=3q+5
It is:
p=3q+5/(10+ r)

Now you should easly understand why it is:
p=3q+5/10q+9r+10

as a rule think
1) ax = by
2) x=by/a