2 of 4 added 975 characters in body

Factor, 113 bytes

I've spent class golfing this and I can't get it shorter.

Translation of: Julia.

[ [a,b] dup append 2 <combinations> [ members ] keep [ first2 coprime? ] filter [ length ] bi@ 2 /i 1 + swap /f ]

Example runs on the first 5 test cases (a value of 1000 causes it to freeze the editor, and I can't be bothered to compile an executable right now):

! with floating point division
IN: scratchpad auto-use {
      1    
      2    
      4    
      10   
      100  
    }
    [ 
      [1,b] dup append 2 <combinations> [ members ] keep 
      [ first2 coprime? ] filter [ length ] bi@ 2 /i 1 + swap /f 
    ]
    map

--- Data stack:
{ 1.0 0.75 0.6875 0.63 0.6087 }
! with rational division
IN: scratchpad auto-use {
      1    
      2    
      4    
      10   
      100  
    }
    [ 
      [1,b] dup append 2 <combinations> [ members ] keep 
      [ first2 coprime? ] filter [ length ] bi@ 2 /i 1 + swap / 
    ]
    map

--- Data stack:
{ 1.0 0.75 0.6875 0.63 0.6087 }
{ 1 3/4 11/16 63/100 6087/10000 }