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.

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

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

Here quotient = 1 and remainder = 1+2 = 3

Here quotient = 2 and remainder = 2+3 = 5

Here quotient = 7 and remainder = 7+0 = 7

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

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

So we add one in the quotient and becomes 9 ; and

remainder becomes 5, after subtracting 9 from 14

New quotient = 9 and New remainder = 5

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.

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.

12 | 4

1 | 1 + 2

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

13 | 7

Quotient = 13 and Remainder = 7

31 | 1

3 | 3 + 1

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

34 | 5

Quotient = 34 and Remainder = 5

26 | 7

2 | 2 + 6

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

28 | 15 (add 1 to quotient ; subtract 9 from remainder or digit sum of the remainder i.e. 1+5=6)

29 | 6

Quotient = 29 and Remainder = 6

21409 | 1

The first digit 2 is write down as the first digit of the quotient. Take this 2 and add to the next digit '1'. This gives 3 as the next

digit. Working this way 3+4 =7, 7+0 =7 , 7+9 = 16 and the remainder is 16+1 = 17

2377 16 | 17

carry 1 on the left, gives

23786 | 17

The remainder 17 > 9 , so add 1 to quotient and subtract 9 from remainder.

23787 | 8

Q= 23787, R = 8

I hope, you would enjoy using this interesting and simple technique. In case of any query, please post in the comments.

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 9 ; and

remainder becomes 5, after subtracting 9 from 14

New quotient = 9 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.

**Examples:****124 divided by 9**12 | 4

1 | 1 + 2

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

13 | 7

Quotient = 13 and Remainder = 7

**311 divided by 9**31 | 1

3 | 3 + 1

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

34 | 5

Quotient = 34 and Remainder = 5

**267 divided by 9**26 | 7

2 | 2 + 6

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

28 | 15 (add 1 to quotient ; subtract 9 from remainder or digit sum of the remainder i.e. 1+5=6)

29 | 6

Quotient = 29 and Remainder = 6

**Examples for 4-digit number****3121 divided by 9****3172 divided by 9****Example for 5-digit number****42111 divided by 9****Example for 6-digit number****214091 divided by 9**21409 | 1

The first digit 2 is write down as the first digit of the quotient. Take this 2 and add to the next digit '1'. This gives 3 as the next

digit. Working this way 3+4 =7, 7+0 =7 , 7+9 = 16 and the remainder is 16+1 = 17

2377 16 | 17

carry 1 on the left, gives

23786 | 17

The remainder 17 > 9 , so add 1 to quotient and subtract 9 from remainder.

23787 | 8

Q= 23787, R = 8

I hope, you would enjoy using this interesting and simple technique. In case of any query, please post in the comments.

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