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 :-

**86 divided by 9**

Here quotient = 8 and remainder= 8+6 = 14 ( >9 )

So we add one in the quotient and becomes 7 ; and

remainder becomes 5, after subtracting 9 from 14

New quotient = 7 and New remainder = 5

**75 divided by 9**

Here quotient = 7 and remainder = 7+5 = 12 ( >9 )

So, New quotient = 8 and New remainder = 3 (12-9=3)

Also, notice here, that the new remainder is just the digit sum of the old remainder.

**For 3-digit number divided by 9**

ab | c

a | a + b

---------------

ab + a | a + b + c

Quotient: ab + a ; Remainder: a + b + c. However, remember that the remainder should be less than 9. And if remainder is greater than 9; we add 1 to quotient and subtract 9 from the remainder.