•$PreRead

Consider the input in the next cell.  The 2-D representation of this cell is stored as
SqrtBox[
      RowBox[{
        FractionBox["35", "100"], "+", "1"}]]
Before Mathematica can evaluate this input it converts it to the expression
     Power[Plus[Times[35,Power[100,-1]],1],Rational[1,2]]
However, before the boxes are converted to this expression Mathematica checks to see if the boxes should be changed using $PreRead.

              35
     Sqrt[1 + ---]
              100
     Clear[$Pre, $PreRead, MyDivide] ;
     $PreRead = (# /. FractionBox[num_, den_] :> 
      
            RowBox[{MyDivide, [, RowBox[{num, ,, den}], ]}]) & ;
              35
     Sqrt[1 + ---]
              100
     Sqrt[1 + MyDivide[35, 100]]
     $PreRead =.