Vedic Math - Divsion by 9

Let us learn, how to do 'Division' operation using 'Vedic Math'. Conventionally, we do it like following:

Divisor ) Dividend ( Quotient
                ---------
                ---------
             _________
             Remainder

However, in the Vedic process, the format is
Divisor ) Dividend
                --------
           __________________
           Quotient | Remainder

Let us first start with one of the special case of division i.e. Division By 9, a very interesting and simple technique.

When dividing by 9, the remainder is always the digit sum of the original number.

For 2-digit number divided by 9 
To divide ab by 9 : Rewrite ab as a | b . The quotient is a, and the remainder is simply a + b.

    a  |  b
        |  a
    ---------
    a  | a + b

Examples: 

12 divided by 9
Here quotient = 1 and remainder = 1+2 = 3

23 divided by 9
Here quotient = 2 and remainder = 2+3 = 5

70 divided by 9
Here quotient = 7 and remainder = 7+0 = 7

Now, let us discuss the cases when remainder is greater than 9 :-