# 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

I worked out this formula and put q as the subject but i got q equals 100p

over 1-P, is this correct

How do you know when exactly to factorise?

thank you for your help, you gained me an extra 9% in my exam

I got 92%

Let’s hope this is in my exam tomorrow then!!

If I get -100p/1-p, is it right. if right, how?

Thank you sir 😀

thanks a lot this helped loads! you explained in a really simple

understandable way, great video!

Thank you so much this help me pass my maths exam

really helped me. thanks

Teaching better than ma teacher tnx

This video really helped me and I am struggling in Maths a bit. So thanks a

lot

I need to make d the subject o the formula

make t the subject p=3-2t

—-

4+t

Thanks a lot man really helped me out as i have a test coming up. Ive

subscribed and liked.

I really like it how you reply to everyone and try to help, even if they

say your channel is bad :D. You’re an amazing person, thank you very much.

Thank you very much, helped quite a bit. Subscribed and liked

could you possibly do a video on an a grade question as i am struggling

with those type of questions. Thanks>

good video and helpful

very helpful! Thankyou

Thanks Simon. Studying Astronomy with no Maths background has been really

tough. Have to do a lot of these. Would love to give you some even more

complicated equations to see you work those out 😉

thank you so much ! i was so confused but this has just made everything way

more clear x

Thank you so much, you are a great teacher. Better than my maths teacher in

fact.:)

thanks sir

Excellent, thank you for that video. Helped loads! Definitely leaving a

like!

Basically a nice guy who dedicates his time helping people. Thanks for

this.

Great video! I’m meant to be revising for our upcoming maths exam and I

couldn’t find anything on this topic that had actually helped me!

this helped lots, thanks

You genius. You legend. I’ll remember that for later exams

OMFG THANK YOU

i love you u just saved my face froma detention thx

The you just saved my neck!!!:)

Hello Simon, I am having trouble with this question..

Transpose the following equations, and solve by substitution:

”y = mx + c for m, and solve by substitution when y = 2, x = 3 and c =

5”

Any help would be appreciated. Thanks!

Omg I have been looking everywhere for a clear cut tutorial like this thank

you so much it really helped

Great Video! Despite being in top set maths, this has always been a topic

that i have found difficult, your video helped clear up the points for me,

although i think it is a little harder when the value on the top is not

alone, e.g in your example it would be something like 8Q-3..

Excellent, thank you for that video.

Thanks so much i did not get it at all until your tutorial

It didn’t help

everybody put the CAPTION english substitles LOOK WTF says really guys

look!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Thanks, this really helped

Do you have any videos on solving difficult equations? I got this question

in a past paper I was doing and I’ve got no idea where to start. Here is

the question:

Solve: 3/x -1 – 4/x+2 = 2

The question is worth 7 marks and I don’t know how to do it. Could you help

me or make a video on it? Thanks!

Thanks for posting this is the clearest video on this topic!

thank you very much. very usefull

I get the explanation above, but pls pls can somebody give me an step by

step explanation of this equation:

It would help with your learning too!

I need to make *Y* the subject. *2y – 3x = 9*

Thank you!

Thank you so much, I couldn’t get this no matter what in my lessons, but

something just clicked when I watched this.

I have a test tomorrow but thanks so much.I understand it now. i cant

stress the ‘so’ much

Earned another subscriber

Thank you sooooo much!

I was really struggling with this but you’ve made it a whole lot easier for

me to do my test tomorrow!

Thanks a million times

WAit wait i used this technique for a different question, I got to

yw+6=x^2

is the next step for me to divide both sides by x?

which would leave me with yw+6 over x = x?

This guy is a lad

What kind of heartless basterd can you be to dislike the video

You’re extremely helpful, I wouldn’t say I’m bad at maths in general, I’ve

just always struggle with this!

Thank you sir!

Thank you for the help I have test tomorrow

I HATE MATH!!!!!!

pls help me with dis equation i have a test tomorrow x’2_26x+25=0

You helped me with this and now I am ready to do my math test

I’m kinda struggling with this algebra question and I’d be grateful if you

could offer some assistance. how can I make B the subject of this formula:

T=3(390s+90l+10b). Thank u.

How do you do v X v= u X u + 2as, they don’t explain it

I have been reading text books and looking at web pages to try to figure

out the correct process for changing the subject of a formula. I then

clicked on a link to this video and I just got it… instantly! It all

makes sense now thank you Simon.

z=(4 times( bracket v-2 all over 8) close bracket) 2 Simone can you please

help me out with this? and is this a C grade or higher/ thanks

and if you have more video of changing subject please let know

hi Simon.

thanks for the video i was completely lost in the classroom by watching

this video has actually open my mind

good

4:48 If “N” was 30, it would be 3,000(3 thousand) and not 30,000 thousand,

right?

Great vid found this really helpful

Hello, I understand what you have done. But you didn’t say why you did it

in the order that you did. Are there specific rules to say that division,

multiplication, subtraction, addition must be done in a certain order? For

example, for the equation of a straight line… y=mx+c, I want to change

the subject to ‘x’. If I subtract ‘c’ from both sides first I get y-c=mx,

then I divide both sides by ‘m’, so I get y-c/m=x….however if I start by

dividing both sides first I would get y/m=x+c and then I would subtract the

‘c’ from both sides, so I get y/m-c=x….so 2 different answers. I’m

guessing there’s a rule I should be following, but I don’t know what it is?

Um how do you get the “minus 1″ from ? I mean the one in q( p – 1)

so… if i post my hw, will you do it for me? 😀

How do you make q the subject?

P= q

——– + 2r

7

Help please if you do see this can you show working out of how you did it

Wow! This was so helpful! Great video. Thank you!!!

Struggled on this for ages! Thank God I clicked on your video! Awesome

video! God bless you!

Thankyou You’re a life saver

so you dont have to work out the left hand side? you just show what you are

doing to it. if anyone understands what i mean

How would I change the subject to U in this formula? X=1/2 (u + v)t

Thank you

I’ve just started Year 11 and I really want an A* in Maths! Hopefully

watching your videos and practicing will help me get better

What if the question is n= -3h+40. (Difference being its a minus)

———-

100.

when factorising is there a trick to knowing if its minus plus and they go

i need work out how rearrange formulae with 2 values the same

Thank you so much !:D

Thanks a lot! Really helpful for tomorrow morning. Exam!

Glad and faint for this video seen as my GCSE is Monday morning

Wish I had found your videos months ago…. my exam is Monday…. eeek..

(and the last time I studied maths was 1987…..god help me!!)

I’m only in year 7 in Australia and this was really helpful!

Great video, this really helped me out (especially as I find this really

tricky). I’ll admit I had to re-watch the video a couple of times mainly

because I didn’t quite get it! Again great great video +1

How do you make a the subject if there’s brackets like M= (1+a) ₃

How come you don’t minus q from the left hand side when you minus q from

the right hand side

Thanx alot it really helped me!!!!!!!

30 x 100 =3000 not 30000.

Great video! very useful! Thank you

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”

thanks a lot for this , I got a GCSE mock next week , glad I finally

understood this

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 ?