# How to change the subject of a formula

## How to change the subject of a formula. A formula is a special equation which deals with ‘variables.’

Variables are bits of information *that can change* each time you deal with the formula.

For instance, one of the best known formulas is:

Speed = Distance / Time … and we use it every time we go somewhere.

If you’re driving at 30 miles per hour – the numbers can be put in place of the words:

Speed = Distance (30 miles) / Time (every 1 hour)

or,

Speed = 30 miles / hour

Exam questions, that are based around this equation, usually ask you to work out one of the ‘terms.’ The questions are usually along the lines of:

- How long does it take to travel 60 miles at a speed of 120 miles per hour?
- How far have I travelled if I walk at 4mph for 3 hours?

- there are only three variables and
- the three variables are all directly, or proportionately, related

Unfortunately it can be a little more difficult to change the subject (the first bit) to another part of the formula – particularly when there doesn’t seem to be a direct relationship.

### Watch the videos and try the quick test.

#### Click here to try the Quick Test Rearranging Formula

Learning how to change the subject of a formula can be important depending upon what we are looking for; or different interpretations of the same thing. For instance in the UK we use degrees Centigrade to measure temperature, in America they use degrees Farenheit.

If you want to convert between Centigrade and Farenheit, both these formulas contain the same information – although each have different subjects:

Follow these steps when learning how to change the subject of a formula:

- Always work down the page with the equals sign in the middle
- Deal with terms in the correct order (use BIDMAS: Brackets, Index (sometimes Order), Division and Multiplication together, Addition and Subtraction together
- Always keep the formula in balance, write each side what you are doing
- Don’t lose track of what you are trying to achieve!

Watch the videos on YouTube;

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Filed in: Foundation • Maths Videos

Thank u so so so much! My end of Year 10 exam is tomorrow and you really

saved me! :):)

where can i find a more complicated question

Man, it’s so much easier when it’s put into context and it’s in front of my

eyes. I got an A in my mock exam and there was a question like this that I

got wrong. Thanks for the help! + Earned a sub!

thanks ,you are a genius

This was useful.

This is great!!! Helped me a lot much appreciated

Thank you so much, i have an end of year test tomorrow and this helped a

tonne

Thanks mate, taught it better than my lecturer

thank you so much

Going in to an Earth sciences degree next year and have not studies maths

since 2007 (My GCSEs) so I am relearning as much as I can before I begin.

This actually really helped me figure this out

thank you so much this video was very helpful. i am at college doing higher

level is there any anther video in higher level in youtube.

thanks

Once again great vid, thanks for the help!!!

Thanks for the vid – has really helped me understand this topic in

preparation for my end of year test!

When at the stage where you have PQ=Q+100P, my next steps were: (-Q)

PQ-Q=100P then (/P) PQ-Q/P=100. Is this still correct?

U r FAB!!!!! i tried all over the world trying to get this stuff in my head

and finally now understand to due to YOU #THANKS SOOOOO MUCH!

Thx so much I understand it now I have a end of term test next week.

I hate this question, I always get it wrong on the Grade B test. I got

every question right except for this one because I wrote

a=sqrt b² / c²

instead of

a=sqrt b² + c²

and the question was

“Rearrange the formula to make a the subject of a² – b² = c ²”

Thank You so much Saved my life!!!

Thanks your a life saver.

Thanks, this really helped me! i couldn’t understand my teacher but you

took time and broke it down, taa . (:

Im not sure if Im being stupid but at 4:50 did he say that 30×100 was

30,000?

Thanks, helped alot!

thanks so much this really helped!

Thanks a lot man . You teach in a very simple and nice way. Keep it up!

Helped so much thanks!!

Thanks great help I wont have to struggle with maths again now ive found

your channel!!!

helped so much thanks m8

Thanks for the help.

Great help, cheers mate

I’m in year 9 and there’s so many people in my year i’ve been put into the

highest year 10 group which is very hard and intimidating, this has helped

me feel so much more confident thanksss

Thanks,it is very helpfull

Thank you so very much!

Absolute champion! You explained it slowly and thoroughly and all of a

sudden it clicked! Thanks mate you’ve helped alot!

that helped so much i had homework on it.

Please like and leave a comment!

Visit http://www.mathswrap.co.uk for real maths, tips and techniques.

Thanks this will help me loads with my revision for my GCSE

mocks in January

Wow this been very helpful! I am redoing my maths GCSE’s and my tutor

hasn’t really explained this very well. Now I feel more knowledgeable

Hi, I’m in year 8 and this video explained everything to me! It was exactly

what I needed for my exam preparation!

Thanks for the comment and all best with your studies

grateful for you and your videos, very relatable. thank you! brilliant for

exams

Will do…I’ll let you know when posted. Rgds S

Hi, is there any possibility of requesting a video on Solving Quadratic equations? Thanks

Hi – there’s a couple of examples on Mathswrap co.uk . Visit maths help, look for quick tests and there’s one on rearranging formulas. Good luck !

just wondering could you give an example of an A to A* question becausse i have an EXAM coming up and im doing A to A* so please reply so i have an idea of what’s coming up.

Thanks

Hi – you’d need a bit more information to solve this. Maybe a way of finding values of some of the variables (x, m, n or p), or sometimes another equation that lets you work simultaneously. If you can post any more detail I’d be happy to help.

All best

S

Hey, I have a question, how would I go about solving x/m – x/n = 1/p

Please post, pin, tweet, like or subscribe!

Glad to help

Also, I have to say that you are a brilliant teacher, and I think that the fact that you are nice an slow makes what you say much easier to understand.

Thanks you very much! This was really helpful for my homework.

Thank you

Hi Rebecca

Bit of a difficult question, although you could say it as 100N-40 all over 3. The ‘all’ is important as you could misread your statement as 100N – 40/3. If you prefer to write it might be better to use brackets so:

h = (100N – 40) over 3

Hope this helps and thanks for the question.

Kind Regards

S

hi im wondering if you can also write this as h=100N-40 over 3?

Thanks so much, really helped. Good teacher you are, slow but surely explaining the solution. I’m confused on x = 5(a+b) [make b subject] at the moment, i’ll get it shortly though, thanks again

thanks

im in year 7 and ive got level 7?8 changing the formala

That’s great and thanks for your comment

Thanks for the video. I will subscribe and hope to find more great Algebra videos.

Thank you it really helped

100N is the same as 3h + 40 – the main thing is to keep in balance. There’s some more info on MathsWrap – How to change the subject of a formula. Hope it helps and really pleased you’re having a go. All best S

So 3h is the same as your explanation with 100N in the video!

Ah – that’s great – glad it helped.

Yes, thanks! I was thinking in your direction plus another. Did not want to get confused in my thinking.

Hi David – thanks for the question. The values of h and N can change – so 3h (which is 3 x h) could be any number times 3. If you divide both sides by 3 + 40 the 3 is ‘three times something’ and the 40 is ’40 added to something.’ Unfortunately they are completely separate ‘terms’ so you can’t treat them equally. Hope this helps? Kind Regards S

Why cant h = 100N divided by 3+40 ? To make h the subject!

100N = 3h + 40 can you not divide both sides by 3 + 40 ?