I observed that the digital root of an 'incorrect division' obtained by dividing a number in a 'special way'/'particular manner' and the digital root of the correct division are always same.
While obtaining first digit of the incorrect division deduct '1' from the correct division digit. Just do this only for the first digit in the division, the remaining division must be carried according to rules of division. e.g. In 125/5 the correct division is 25 and the special incorrect division is: 125/5=196. If we observe the digital roots of correct and 'special incorrect division', we find that they are same that is '7' This fact holds true for any number. Some more examples are,
1] Special Incorrect division 11/2 = 41.5 has digital root 4+1+5=>10=>1+0=>1
Correct division 11/2 = 5.5 has digital root 5+5=>10=>1+0=>1
2] Special Incorrect division 81/3 = 198 has digital root 1+9+8=>18=>9 Correct division 81/3 = 27 has digital root 2+7=>9
How does this happen? Any mathematical proof?