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Thread: Transposition of Formula

  1. #1 Transposition of Formula 
    The Doctor Quantime's Avatar
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    Hi guys, I'm having trouble learning the conecpts of transposing equations, I can't get my head around it and would greatly appreciate some help.



    For some reason I cannot transpose this simple equation. Whenever I do, I get odd numbers.

    For their values I used:

    P = 50
    W = 100
    t = 2

    I know that I need to end up with

    Yet no matter how hard I try when I transpose I end up with

    Where am I going wrong?

    Thanks in advance.
    QT


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  3. #2  
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    P=W/t

    multiply both sides by t

    tP = W

    divide both sides by P

    t = W/P


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  4. #3  
    The Doctor Quantime's Avatar
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    I got that after you helped, thanks. I'm still having problems with understanding the rules of transposition.

    I'm having difficulty with: x x x

    The is actually x with a lower case l tagged to it, it isn't linked to on its own.
    3.141 is pi, I haven't got the symbol for it on this forum.

    Could you also please put this transposition into stages, why you moved it, why you moved the specific values in specific orders, (for instance if you move first, please state why).

    I understand that you do the opposite to mathematical signs when you move them across and I also understand that you have to do the same to the same side. I don't know the rules of why you move certain values first, and where abouts you put them on the other side.

    For instance, if I move to the same side as and divide it by , I thus have to divide the original side by as well right?

    But what happens after that? Where abouts do I move f to after? Above on the left hand side? Or along side it? The same for pi and 2.

    I'm sure transposition of forumla is simple, yet I need to know the rules and how you do it.

    Help is greatly appreciated.

    Thanks!
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  5. #4  
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    Quote Originally Posted by Quantime
    I got that after you helped, thanks. I'm still having problems with understanding the rules of transposition.

    I'm having difficulty with: x x x

    The is actually x with a lower case l tagged to it, it isn't linked to on its own.
    3.141 is pi, I haven't got the symbol for it on this forum.

    Could you also please put this transposition into stages, why you moved it, why you moved the specific values in specific orders, (for instance if you move first, please state why).

    I understand that you do the opposite to mathematical signs when you move them across and I also understand that you have to do the same to the same side. I don't know the rules of why you move certain values first, and where abouts you put them on the other side.

    For instance, if I move to the same side as and divide it by , I thus have to divide the original side by as well right?

    But what happens after that? Where abouts do I move f to after? Above on the left hand side? Or along side it? The same for pi and 2.

    I'm sure transposition of forumla is simple, yet I need to know the rules and how you do it.

    Help is greatly appreciated.

    Thanks!
    If I understand the equation,



    divide both sides by 2pi

    divide both sides by l and we have singled out f, or

    divide both sides by f and we have singled out l

    Oh, \pi= \dfrac{a}{b}= 2\times 3=

    I did each step in no particular order. It's simply just reverse operations, and all operations done to one side must be done to both sides, as you said. The best way to think about it is to take the side that has the most 'stuff' and to do whatever operations necessary to cancel out whats on that side save for one element, normally a variable. the example you gave can be transposed in multiple ways, all depending on which variable you want to define in terms of the others. The constants (2pi in your example) are always going to be moved away from whatever you're defining.
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  6. #5  
    The Doctor Quantime's Avatar
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    Excellent! Thanks Arcane. I actually did this transposition before you posted, I created values to help me and it worked a treat, and your analogy works spiffing.

    I ended up with it looking a little different:



    Not much different though. That helped me out thanks again...

    There is a slight edge to my understanding however and it works along side the damn dividing part of transposition.

    If you look at my first post I had trouble transposing a simple Power formula starting with a division equation. I had done some multiplication and easily transposed that. I have narrowed it down to division being my weak point because now again, like before I am stuck with dividing. I have tried transposing this formula and have had no success.... I have also been using a calculator with values I made up and letting it do its 'math rule' thing of BODMAS to help, yet it hasn't... my key challenge is transposing this forumla:

    c

    I want to get C on it's own and to be frank, I haven't the foggiest.

    Like my , I am having trouble. I have tried all sorts and had no success.

    I had tried shifting as a whole but that did not work.

    If it helps I had assigned these values:


    1= 1
    2 = 2
    = 3 (for simplicity's sake)
    F = 5
    C= 10
    c = 75

    I got 75 for c because of using my calculator in the way to solve that forumla as it is written (bodmas obviously).

    So again, asking for help, what is the method to transpose this formula when division is involved and the subject (C) is below that division and multiplied by something else at the same time? I am confused as if I am allowed to shift values under '1' without messing up the formula.

    Cheers!
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  7. #6  
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    Multiply the whole equation by C.
    Divide the whole equation by xc.
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  8. #7  
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    Quote Originally Posted by Quantime
    I got that after you helped, thanks. I'm still having problems with understanding the rules of transposition.
    Your problem is likely that you are thinking in terms of rules of transposition. Just apply the ordinary simple laws of algebra -- associative, commutative and distributive properties involving addition and multiplication and work it our for yourself. Forget memorizing rules.
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  9. #8  
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    Quote Originally Posted by Sindrato
    Multiply the whole equation by C.
    Divide the whole equation by xc.
    Is this correct? I have used this formula with my values and do not get the same value.

    Dr.Rocket, I jumped straight onto this transposition with very little knowledge of algebra. I don't know associative, commutative and distributive properties in algebra, what are they?
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  10. #9  
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    Those are things like:

    associativity:
    (X * Y) * Z = X * (Y * Z)

    commutativity:
    X * Y = Y * X

    distributivity:
    X * (Y + Z) = (X * Y) + (X * Z)
    and
    (X + Y) * Z = (X * Z) + (Y * Z)

    These rules always apply if * represents ordinary multiplication and + represents ordinary addition. Tricky words, but I guess you have already used these properties without knowing their names.
    "Complexity is stupidity disguised as intellect."
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  11. #10  
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    Quote Originally Posted by Quantime
    Quote Originally Posted by Sindrato
    Multiply the whole equation by C.
    Divide the whole equation by xc.
    Is this correct? I have used this formula with my values and do not get the same value.

    Dr.Rocket, I jumped straight onto this transposition with very little knowledge of algebra. I don't know associative, commutative and distributive properties in algebra, what are they?
    He is absolutely correct
    Wise men speak because they have something to say; Fools, because they have to say something.
    -Plato

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  12. #11  
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    Your starting values were wrong. It was
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  13. #12  
    The Doctor Quantime's Avatar
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    Thanks for all the help guys, I can help some of my classmates with this transposition now, thanks you've really helped me and my mates.
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  14. #13  
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    Quote Originally Posted by Arcane_Mathematician
    Quote Originally Posted by Quantime
    I got that after you helped, thanks. I'm still having problems with understanding the rules of transposition.

    I'm having difficulty with: x x x

    The is actually x with a lower case l tagged to it, it isn't linked to on its own.
    3.141 is pi, I haven't got the symbol for it on this forum.

    Could you also please put this transposition into stages, why you moved it, why you moved the specific values in specific orders, (for instance if you move first, please state why).

    I understand that you do the opposite to mathematical signs when you move them across and I also understand that you have to do the same to the same side. I don't know the rules of why you move certain values first, and where abouts you put them on the other side.

    For instance, if I move to the same side as and divide it by , I thus have to divide the original side by as well right?

    But what happens after that? Where abouts do I move f to after? Above on the left hand side? Or along side it? The same for pi and 2.

    I'm sure transposition of forumla is simple, yet I need to know the rules and how you do it.

    Help is greatly appreciated.

    Thanks!
    If I understand the equation,



    divide both sides by 2pi

    divide both sides by l and we have singled out f, or

    divide both sides by f and we have singled out l

    Oh, \pi= \dfrac{a}{b}= 2\times 3=

    I did each step in no particular order. It's simply just reverse operations, and all operations done to one side must be done to both sides, as you said. The best way to think about it is to take the side that has the most 'stuff' and to do whatever operations necessary to cancel out whats on that side save for one element, normally a variable. the example you gave can be transposed in multiple ways, all depending on which variable you want to define in terms of the others. The constants (2pi in your example) are always going to be moved away from whatever you're defining.

    It is so complex, can say the detailed point thanks very much
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  15. #14  
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    ok, hey guys, i've been reading these posts and they helped me with some of my formulas... but there are other formulas i cant understand like: x=y-2/y-3, express y in terms of x. i appreciate all attempts in aiding me with this question. Thanks.
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  16. #15  
    Ots
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    Multiply through by y and then put it in quadratic form (carefully) and apply the quadratic formula.
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