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Making a variable the subject

  1. Apr 29, 2009 #1
    Hi. With the equation:

    A = B x (C / D) x (E x F)

    To make D the subject would it be:

    (C / D) = B x (E x F) / A

    D = (B x (E x F) / A) x C

    ?

    Thanks.
     
  2. jcsd
  3. Apr 29, 2009 #2
    If you were to isolate C/D as you did in your first step, then A should have been the numerator of the right side. While isolating, technically you divide both sides by the same expression (in this case B x E x F to eliminate them from the side where C/D is).

    A simpler method would be to apply the associative property of multiplication and just lump B, C, E, and F together so that you end up with (B x C x E x F)/D and isolate D from there.
     
  4. Apr 29, 2009 #3
    So assuming the commutative properties: D = B x C x E x F / A?
     
  5. Apr 29, 2009 #4

    HallsofIvy

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    No. To isolate C/D, because in your equation it is multiplied by B and (E x F) you must divide both sides by B x (E x F): C/D= A/(B x (E x F)). Then, to get the D into the numerator, "invert" both sides: D/C= (B x E x F)/A.

     
  6. Apr 29, 2009 #5

    So assuming D/C = (B x E x F) / A would it not be D = (B x E x F) / A x C ?


    Thanks.
     
  7. Apr 29, 2009 #6
    No, you had it right in your previous post;

    you multiply both sides by C in order to get rid of the C on the left hand side which makes the right hand side.

    ((B x E x F) / A ) x C which as you rightly said before is equal to

    (B x E x F x C) / A
     
  8. Apr 29, 2009 #7
  9. Apr 29, 2009 #8

    HallsofIvy

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    No, it would not! In order to eliminate the C on the left side, you must multiply by C, not divide by it. The way you have written that, C is in the denominator. If you mean D= [(B x E x F)/A] x C write it as D= (B x E x F x C)/A.
     
  10. May 26, 2009 #9
    I have a question on this one: would it be OK when you are changing the subject of a formula to have the subject on the right side of the formula?

    Let's suppose you have the following formula:

    A + D = 2*E + G

    and I want G to be the subject of the formula. Is it OK if I write the answer like:

    A + D - 2*E = G ?

    Some mathematicians say it is OK to provide the answer in that fashion, but I was taught in high school you should always write the subject on the left side, like this:

    G = A + D - 2*E

    Am I wrong?
     
  11. May 26, 2009 #10

    cepheid

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    It makes no difference.
     
  12. May 26, 2009 #11

    djeitnstine

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    Its just the same way to express the same thing, neither is right nor wrong. You haven't violated any rules of math.
     
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