Rearranging Formulae - when the variable is on the bottom of a fraction?

Hi everyone,

Can someone please help me solve what feels like a huge obstacle but probably has a very simple explanation?

I'm struggling with rearranging formulae when the variable I am working out is at the bottom of a fraction.

For example, 5s = D + 3w
8v

I need to rearrange this so that 'v' is the subject.

I can rearrange this to the point where I reach 8(5s - 3w) which would be 40s - 24w = D
v

Now, this is where I am struggling to understand the principle where you just swap 40s - 24w and v so that the final answer to this formulae would be v = ___D___
40s - 24w

Can someone tell me why we swap them to get to this answer?

If we were working out 'D' as the subject, then we would multiply 'v' to 40s - 24w, and I am OK when working out the variable on top of the fraction, but when we have the variable at the bottom of the fraction, why is it just swapped?

Thank you in advance

(I've attached a photo as my formulae is not formatting properly as text and it looks confusing).

Hi everyone,

Can someone please help me solve what feels like a huge obstacle but probably has a very simple explanation?

I'm struggling with rearranging formulae when the variable I am working out is at the bottom of a fraction.

For example, 5s = D + 3w
8v

I need to rearrange this so that 'v' is the subject.

I can rearrange this to the point where I reach 8(5s - 3w) which would be 40s - 24w = D
v

Now, this is where I am struggling to understand the principle where you just swap 40s - 24w and v so that the final answer to this formulae would be v = ___D___
40s - 24w

Can someone tell me why we swap them to get to this answer?

If we were working out 'D' as the subject, then we would multiply 'v' to 40s - 24w, and I am OK when working out the variable on top of the fraction, but when we have the variable at the bottom of the fraction, why is it just swapped?

Thank you in advance

(I've attached a photo as my formulae is not formatting properly as text and it looks confusing).

Because you can multiply both sides by V and then divide both sides by the W and S thing, to get V = D/ the W and S thing.

You aren't swapping them

40s - 24w = (D/V)

x both sides by V

V(40s - 24w) = D

now divide both sides by (40s - 24w)

V = D/(40s - 24w)