How to change the subject of a formula

February 17, 201343 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 (43)

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    1. Kamran Ahmad says:

      thanks so much this really helped!

    2. Ali Almusawi says:

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

    3. Kristina Herron says:

      Helped so much thanks!!

    4. methaloniangames says:

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

    5. andrew jara says:

      helped so much thanks m8

    6. Ang Rui Yong says:

      Thanks for the help.

    7. Badders Bee says:

      Great help, cheers mate

    8. 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

    9. Winnifred Barbara Parks says:

      Thanks,it is very helpfull

    10. SenurPenguin says:

      Thank you so very much!

    11. EBON1CS says:

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

    12. TheMolovideos says:

      that helped so much i had homework on it.

    13. Simon Deacon says:

      Please like and leave a comment!

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

    14. Jack Higgins says:

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

    15. 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

    16. 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!

    17. Simon Deacon says:

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

    18. Dan McNab says:

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

    19. Simon Deacon says:

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

    20. SofaSwayKoala says:

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

    21. 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 !

    22. 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

    23. 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

    24. HoldingCa says:

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

    25. Simon Deacon says:

      Please post, pin, tweet, like or subscribe!

    26. Simon Deacon says:

      Glad to help :-)

    27. 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.

    28. Natho H says:

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

    29. bzdurki3 says:

      Thank you

    30. 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

    31. Rebecca Broughton says:

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

    32. 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

    33. navin kissoon says:

      thanks

    34. mischigan taylor says:

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

    35. Simon Deacon says:

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

    36. Elmen Ortiz says:

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

    37. Cosmic Paudel says:

      Thank you it really helped

    38. 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

    39. David Camel says:

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

    40. Simon Deacon says:

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

    41. David Camel says:

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

    42. 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

    43. 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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