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 https://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 ?