my compiler says "Error 26: Type mismatch" for the following line:

  changednumber[i] := 'moddivision';

you need to know:
It's a program to change numbers of base 10 to numbers of base 2..36.

 PROGRAM...
 TYPE NUMBASE = 2..36;

 VAR base :NUMBASE;
     number  :LONGINT;
     changednumber :STRING[36];
     i :INTEGER;

 FUNCTION NumToString(x:LONGINT; b:NUMBASE):STRING;

 VAR newdivision :REAL;
     moddivision,divisionnumber:INTEGER;

BEGIN
    i := 0;
    divisionnumber := x;
    newdivision := 0;

   REPEAT
     i := i + 1;
     newdivision        := divisionnumber / b;
     moddivision    := divisionnumber mod b;
     changednumber[i] := 'moddivision';
     newdivision       := newdivision - (moddivision/b);
     divisionnumber        := newdivision;
   UNTIL (divisionnumber = 0);
 END;

 Thanks in advance.

-Daniel

changednumber[i]:=chr(moddivision+48);

You could also use chr(moddivision+ord('0'))

This however, works only up to base 10. For higher bases you need to
define representation for numbers 10.. As the highest base is 36 I think
it is assumed that letters A..Z. You could either use a string constant
that has all the values, or use a condition:

If moddivision>=10 then changednumber[i]:=chr(.... +ord('A'))
                   else changednumber[i]:=chr(moddivision+ord('0'));

Since this is a home work I have left it partially blank.

 PROGRAM ConvertDecimalToBase;
 CONST symbols = '0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ';
 TYPE NUMBASE = 2..36;

 VAR base :NUMBASE;
     number  :LONGINT;
     changednumber :STRING[36];    {too long but makes no difference}
     i :INTEGER;