How to change the subject of a formula

February 17, 201383 Comments

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?
They should be fairly straightforward to answer as
  • 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:

tempconv2.png (357×128)

 

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!

 

Visit other related posts:
  • How to solve linear equations with video examples
  • How to work with arithmetic sequences
  • Numeracy skills – how to work out percentages
  • How to add, subtract, multiply, divide decimals
  • How to add, subtract, multiply, divide fractions
  • Filed in: FoundationMaths Videos
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    Comments (83)

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    1. 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

    2. Tom Griff says:

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

    3. 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 :)

    4. Luke Voller says:

      What if the question is n= -3h+40. (Difference being its a minus)
      ———-
      100.

    5. stephen barker says:

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

    6. stephen barker says:

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

    7. RoxieRofl RozyRetzel says:

      Thank you so much !:D

    8. Samuel Cirdei says:

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

    9. jackster11997 says:

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

    10. 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!!)

    11. Sasha Mader says:

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

    12. 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

    13. WolF_PaC.K says:

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

    14. 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

    15. genious razor says:

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

    16. MAJORSNODGRASS says:

      30 x 100 =3000 not 30000.

    17. Marisol Buitrago says:

      Great video! very useful! Thank you :)

    18. carla egea says:

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

    19. Jason Churches says:

      where can i find a more complicated question

    20. 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!

    21. Tashinga Matunga says:

      thanks ,you are a genius

    22. Claudia Pettifer says:

      This was useful.

    23. GHAZALA JABEEN says:

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

    24. Devil Spartan says:

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

    25. freaker77 says:

      Thanks mate, taught it better than my lecturer :-)

    26. warsame abdi says:

      thank you so much

    27. 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

    28. 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 :)

    29. Joel Williams says:

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

    30. Joel Williams says:

      Thanks for the vid – has really helped me understand this topic in
      preparation for my end of year test!

    31. 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?

    32. 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!

    33. PROSNIPZ says:

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

    34. 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”

    35. JustAnother Uchiha says:

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

    36. Shaun Taylor says:

      Thank You so much Saved my life!!!

    37. allmle75 says:

      Thanks your a life saver.

    38. Elisha Chouhan says:

      Thanks, this really helped me! i couldn’t understand my teacher but you
      took time and broke it down, taa . (:

    39. Tom Tra iner says:

      Im not sure if Im being stupid but at 4:50 did he say that 30×100 was
      30,000?

    40. Lo-Lo Haslam says:

      Thanks, helped alot!

    41. Kamran Ahmad says:

      thanks so much this really helped!

    42. Ali Almusawi says:

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

    43. Kristina Herron says:

      Helped so much thanks!!

    44. methaloniangames says:

      Thanks great help I wont have to struggle with maths again now ive found
      your channel!!! :-)

    45. andrew jara says:

      helped so much thanks m8

    46. Ang Rui Yong says:

      Thanks for the help.

    47. Badders Bee says:

      Great help, cheers mate

    48. 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

    49. Winnifred Barbara Parks says:

      Thanks,it is very helpfull

    50. SenurPenguin says:

      Thank you so very much!

    51. EBON1CS says:

      Absolute champion! You explained it slowly and thoroughly and all of a
      sudden it clicked! Thanks mate you’ve helped alot!

    52. TheMolovideos says:

      that helped so much i had homework on it.

    53. Simon Deacon says:

      Please like and leave a comment!

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

    54. Jack Higgins says:

      Thanks this will help me loads with my revision for my GCSE
      mocks in January

    55. 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

    56. 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!

    57. Simon Deacon says:

      Thanks for the comment and all best with your studies :-)

    58. Dan McNab says:

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

    59. Simon Deacon says:

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

    60. SofaSwayKoala says:

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

    61. 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 !

    62. 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

    63. 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

    64. HoldingCa says:

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

    65. Simon Deacon says:

      Please post, pin, tweet, like or subscribe!

    66. Simon Deacon says:

      Glad to help :-)

    67. 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.

    68. Natho H says:

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

    69. bzdurki3 says:

      Thank you

    70. 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

    71. Rebecca Broughton says:

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

    72. 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

    73. navin kissoon says:

      thanks

    74. mischigan taylor says:

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

    75. Simon Deacon says:

      That’s great and thanks for your comment :-)

    76. Elmen Ortiz says:

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

    77. Cosmic Paudel says:

      Thank you it really helped

    78. 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

    79. David Camel says:

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

    80. Simon Deacon says:

      Ah – that’s great – glad it helped. :-)

    81. David Camel says:

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

    82. 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

    83. 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 ?

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