Question 39846
Vp over VS = Np over Ns          this transposes to Vs= Vp x Ns over Np

The general rule for solving equations is "whatever you do to 
one side of the equation you must do to the other side".

You have Vp/Vs = Np/Ns
You want to solve this for Vs so you need to get Vs into the numerator.

Multiply both sides by Vs to get:
Vs(Vp/Vs)=Vs(Np/Ns)
Cancel the Vs's on the left side to get:
Vp = Vs(Np/Ns)

Now multiply both sides by (Ns/Np) to get:
Vp(Ns/Np)= Vs(Np/Ns)(Ns/Np)

Cancel the Np's and the Ns's on the right side to get
Vp(Ns/Np)=Vs

This is the "transformed" equation you want.

You may think this is very cumbersome.  I assure you
there are quicker ways to reach this final goal but 
you wanted to see all the steps.
Cheers,
Stan H.