1. ## Isolating Variables

I am studying for a test and need a variable of a equation isolated to one side.

The equation is:

t/360 = s/2pr

I need the variable r by itself.
How would I go about doing this?
Thanks!

2. Ok there are a few ways you could do this, so I'll just pick one.

You have $\displaystyle \frac{t}{360}=\frac{s}{2pr}$

Let's cancel out the 2pr in the denom. of the RHS by multiplying everything by 2pr.

Thus $\displaystyle 2pr \times \frac{t}{360} = s$

Let's use parentheses though to show the multiplication (just to be more formal)

$\displaystyle (2pr) \left( \frac{t}{360} \right) = s$

Follow?

Now let's rearrange some terms to get r alone. The above equation is equal to.

$\displaystyle (r) \left( \frac{2pt}{360} \right) = s$

Now this next part might seem tricky to you. We are really one step away from isolating r. We must simply divide by $\displaystyle \frac{2pt}{360}$ and on the LHS we will just have r and on the RHS we'll get the rest of the terms. So...

Can you simplify the rest?

$\displaystyle r = \frac{s}{\left( \frac{2pt}{360} \right)}$

3. $\displaystyle \dfrac{t}{360} = \dfrac{s}{2pr}$

$\displaystyle \dfrac{2tpr}{360} = s$

$\displaystyle \dfrac{tpr}{180} = s$

$\displaystyle tpr= 180s$

$\displaystyle r= \dfrac{180s}{pt}$