Method 11

Method 10

Division By 9

This  method is based on the sutra " Nikhilam Navatas' Caramam Dashath "which means ' all from 9 and the last from 10 ' .
Explaining the method with the help of an example .
Example 1 : - Divide 341 by 9 .

Answer : -

Step 1 : -

Write the first digit from left as it is .
i.e.
Obtained digit = 3
Step 2 : -
Now add First digit to the next digit .
i.e.
                 3 + 4  =  7
and write it to the right of above obtained digit .
Obtained digit =   37

Step 3 : -

Now add the digit obtained in previous step to the next digit .
i.e.
              7  +  1   =   8
The quotient is the digit leaving the last obtained digit .
Take the remainder as the last digit thus obtained .
If last digit is 9 then increase the quotient by 1 and make the remainder as zero .
Hence
Quotient = 37        Remainder = 8.

Example 2 : -  Divide 40214  by 9 .
Answer : -
Step 1 : - 
Obtained digit = 4
Step 2 : -
Add next digit
i.e.   4  +   0  =   4
Obtained digit =  44

Step 3 : -

Add next digit
i.e.
            4  +  2  =  6
Place it to the right
Obtained digit = 446
Step 4 : -
Add the next digit tot the previously obtained digit .
i.e.
              6  +  1  =  7
Obtained digit = 4467
Step 5 : -
Add the next digit tot the previously obtained digit .
i.e.
               7 + 4 = 11
Subtract as many 9 from this as posssible and add the number of subtracted nine
to the quotient .
11 -  9.a (value of a is 1)
11 - 9 = 2
Hence
Qotient = 4467 + a = 4468
Remainder = 2