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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 :-
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.
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 :-
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.
