Consider the following procedure for dividing the three-digit number by :
Write down the number formed by the first two digits, namely .
Multiply this by to get .
Add to this, the units digit of (the original number), obtaining .
Then divide it by to get with a remainder of .
Add this result (, remainder ) with (the first two digits of the original number) to get your answer: , remainder .
Thus divided by equals with a remainder of .
Does this method always work for three-digit numbers? Why, or why not?