Operate over list of pure functions

This perhaps:

Function[{a, b}, a[#]/b[#] &] @@@ {{a, b}, {c, d}, {e, f}}
(* Out: {a[#1]/b[#1] &, c[#1]/d[#1] &, e[#1]/f[#1] &} *)

Mr.Wizard's way of writing it (see comment) looks like this in the frontend:

You can almost always turn to replacement patterns when you need to transform expressions:

Cases[
  {{a, b}, {c, d}, {e, f}},
  {x_, y_} :> (x[#]/y[#] &)
]

Click to copy

{a[#1]/b[#1] &, c[#1]/d[#1] &, e[#1]/f[#1] &}

Cases defaults to levelspec {1} so this is safer than using /..

Also:

With[{a = #1, b = #2}, a[#]/b[#] &] & @@@ {{a, b}, {c, d}, {e, f}}

or

x[#]/y[#] & /. {x -> #1, y -> #2} & @@@ {{a, b}, {c, d}, {e, f}}

(* {a[#1]/b[#1] &, c[#1]/d[#1] &, e[#1]/f[#1] &} *)