Rearranging Equations: Making a Variable the Subject

[questions_uk]

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.

 

[Kachiko]

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.

 

[questions_uk]

So assuming the commutative properties: D = B x C x E x F / A?

 

[HallsofIvy]

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

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.

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

?

Thanks.

 

[questions_uk]

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.

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

 

[Chewy0087]

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

 

[questions_uk]

Thanks!

 

[HallsofIvy]

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


Thanks.

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.

 

[topito2]

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?

 

[cepheid]

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?

It makes no difference.

 

[djeitnstine]

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?

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