## 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;

AlphaGaming101 says

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

over 1-P, is this correct

EpicNightBlade says

How do you know when exactly to factorise?

Luca Bentivoglio says

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

I got 92%

Alex Woodward says

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

Zafar Badami says

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

Kabir Ahmad says

Thank you sir 😀

J Holland says

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

understandable way, great video!

Jovan Hubsie says

imnotinnocent says

Thank you so much this help me pass my maths exam

Amdeegamerz says

really helped me. thanks

Afghan BOy xD says

Teaching better than ma teacher tnx

muhammad ali says

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

lot

bee bisto says

I need to make d the subject o the formula

TheAlexMasonShow . says

make t the subject p=3-2t

—-

4+t

David Kennedy says

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

subscribed and liked.

Soroush Hashemloo says

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.

Soroush Hashemloo says

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

Rizwaan Azad says

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

with those type of questions. Thanks>

Rizwaan Azad says

good video and helpful

Emily Trouse says

very helpful! Thankyou

mrjaffa1013 says

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 😉

Maheen Ahsin says

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

more clear x

Michael kemp says

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

fact.:)

Kirt Clarke says

thanks sir

Yishai Lister says

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

like!

Michael Milne says

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

this.

Rebecca Mathers says

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!

Mitchell Hargrave says

this helped lots, thanks

Brandon Saiger says

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

ChickenElBito says

OMFG THANK YOU

Atalaia Sol Lagos says

i love you u just saved my face froma detention thx

CoolPlays says

The you just saved my neck!!!:)

Joshua Dixon says

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!

Aman Marwaha says

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

you so much it really helped

RedfernModelRailway says

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..

Ben Duncan says

Excellent, thank you for that video.

Daniel Follant says

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

Luther Michalski says

It didn’t help

Goldinfinityxi Pegauss says

everybody put the CAPTION english substitles LOOK WTF says really guys

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

Epicnerd73 says

Thanks, this really helped

Epicnerd73 says

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!

cyriptobi137 says

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

ruvindu saunya says

thank you very much. very usefull

Roxy J says

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!

Harry Norris says

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

something just clicked when I watched this.

KrazeProductions says

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

stress the ‘so’ much

Earned another subscriber

kashmala anwaar says

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

Andrei Vaughn says

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?

CumWhore69 says

This guy is a lad

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

Birthday N says

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!

Ali Alkuwari says

Thank you for the help I have test tomorrow

jasdeep sandhu says

I HATE MATH!!!!!!

Balla Abu says

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

Aslan Aslanli says

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

eugene molley says

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.

mancannon90k says

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

Martin Jorgensen says

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.

ali ghamyar says

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

ali ghamyar says

hi Simon.

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

this video has actually open my mind

Bangura Modoulamin says

good

NeronMC says

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

right?

hodgson1928 says

Great vid found this really helpful

V Coates says

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?

TheOrangedestruction says

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

Naynay Neo says

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

niraj bodalikar says

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

Magdalena Garcia says

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

Sonal Hema Patel says

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

video! God bless you!

Orient Express says

Thankyou You’re a life saver

Greatsaiyanman says

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

Tom Griff says

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

Thank you

Oo Laitan says

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

Luke Voller says

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

———-

100.

stephen barker says

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

stephen barker says

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

RoxieRofl RozyRetzel says

Thank you so much !:D

Samuel Cirdei says

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

jackster11997 says

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

Wendy Mae says

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!!)

Sasha Mader says

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

Etienne Purches says

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

WolF_PaC.K says

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

miles barton-black says

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

the right hand side

genious razor says

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

MAJORSNODGRASS says

30 x 100 =3000 not 30000.

Marisol Buitrago says

Great video! very useful! Thank you

carla egea says

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

saved me! :):):)

Jason Churches says

where can i find a more complicated question

Toopsy Woopsy says

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!

Tashinga Matunga says

thanks ,you are a genius

Claudia Pettifer says

This was useful.

GHAZALA JABEEN says

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

Devil Spartan says

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

tonne

freaker77 says

Thanks mate, taught it better than my lecturer

warsame abdi says

thank you so much

joeymediauk says

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

muzhgan qaumi says

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

Joel Williams says

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

Joel Williams says

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

preparation for my end of year test!

gibbo1112 says

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?

AM moses says

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!

PROSNIPZ says

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

JezDayy says

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”

JustAnother Uchiha says

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

understood this

Shaun Taylor says

Thank You so much Saved my life!!!

allmle75 says

Thanks your a life saver.

Elisha Chouhan says

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

took time and broke it down, taa . (:

Tom Tra iner says

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

30,000?

Lo-Lo Haslam says

Thanks, helped alot!

Kamran Ahmad says

thanks so much this really helped!

Ali Almusawi says

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

😀

Kristina Herron says

Helped so much thanks!!

methaloniangames says

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

your channel!!!

andrew jara says

helped so much thanks m8

Ang Rui Yong says

Thanks for the help.

Badders Bee says

Great help, cheers mate

Olivia Mcgann says

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

Winnifred Barbara Parks says

Thanks,it is very helpfull

SenurPenguin says

Thank you so very much!

EBON1CS says

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

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

TheMolovideos says

that helped so much i had homework on it.

Simon Deacon says

Please like and leave a comment!

Visit http://www.3minutemaths.co.uk for real maths, tips and techniques.

Jack Higgins says

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

mocks in January

Alexander Combrink says

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

Jazmin Chloe says

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

what I needed for my exam preparation!

Simon Deacon says

Thanks for the comment and all best with your studies

Dan McNab says

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

exams

Simon Deacon says

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

SofaSwayKoala says

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

Simon Deacon says

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 !

UrbanHDGamingVideo says

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

Simon Deacon says

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

HoldingCa says

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

Simon Deacon says

Please post, pin, tweet, like or subscribe!

Simon Deacon says

Glad to help

Natho H says

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.

Natho H says

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

bzdurki3 says

Thank you

Simon Deacon says

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

Rebecca Broughton says

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

SimoZXGaming says

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

navin kissoon says

thanks

mischigan taylor says

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

Simon Deacon says

That’s great and thanks for your comment

Elmen Ortiz says

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

Cosmic Paudel says

Thank you it really helped

Simon Deacon says

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

David Camel says

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

Simon Deacon says

Ah – that’s great – glad it helped.

David Camel says

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

Simon Deacon says

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

David Camel says

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 ?