Determing the order when moving to the other side of the equation. Sorry if the title is vague. But I don't really know the terms I'm looking for ( Nor do I know any tags that go with it). I usually end up being confused with the little( and perhaps trivial things ) in math. The following for example:



to



What are the rules that demand it's a.b / ||a||||b|| and not ||a||||b|| / a.b ?

Perhaps this is a silly question. But, What are the rules when moving from one side of the equation to the other?
The general rule is, you can do anything to one side of an equation, so long as you do the same thing to the other side. So, if you have the equation, $$r=st$$ you can multiply both sides by $1/s$ (assuming that $s\ne0$) to get $$(r)(1/s)=(1/s)st$$ which becomes $${r\over s}=t$$ There's no way you can go from $r=st$ to $s/r=t$ by doing the same thing to both sides of the equation.
$x = y \cos \theta$

$x/y = \cos \theta$

$\arccos (x/y) = \theta$

Edit:

$x = y \times z$

$x \div y = z$