Can Someone Show Me Steps On How To Solve This: 1/8=(?)%x5/8

I'm a little confused on how you wrote out the equation.  
I'm assuming what you mean is
1/8 =  x * 5/8 and you want x to be a %.  If that is correct, than this is how you solve.  
You need to get x alone, so you would divide boths sides by 5/8. When dividing with fractions, you are basically just multiplying with its reciprical, which is just the fraction flipped upside down.  So 5/8's reciprical is 8/5.  When multiplying 5/8 by 8/5, you get 1, leaving x by it self.  

When multiplyin 1/8 by 8/5 you get 8/40 or 1/5 (simplest form.)

so x = 1/5.  When you divide 1/5 out you get .20, but that is not a percentage.  After dividing out a fraction, you then move the decimal point 2 places to the left to get a percentage.  So .20 = 20%

Now, to check our work, place 20% in the equation.  

20% * 5/8 = .125  which is 1/8.