Just remember: K(original) = [Product] / [Reactants]
Thus if the reaction is reversed then the original reactants become products and the original products become reactants: K(reverse) = [Reactants] / [Products]
Mathematically this these equations are the inverse of each other:
K(reverse) = 1/ K(original) ======> 1 / { [Product] / [Reactants] } ===> [Reactants] / [Products]
Say, [Product] = 5
[Reactant] = 1
Koriginal = 5/1 This equals 5...
Now for the reverse
K reverse = 1 /(5/1) ===> 1/5 The inverse of the original.
Use my values and double their concentrations and see whats happens...
Product = 5*2
Reactants = 1*2
K(double) = [10]^2 / [2]^2 == 100/4 == 25 Double the concentration equals K(original) squared! 5 squared is 25