Division of any number with 9 in seconds

vedic math trick to divide any number easily with 9.

With this method, you'll be relaxed from remembering tables. No complicated subtraction and only single or at most 2 step process neede to be followed here.

divisor will be 9 here and the number which is to be "divided " is the dividend.

Method 

  1. Differentiate last digit of dividend with slash (/) for remaining digits.
  2. write compliment under divisor or just remember it.
  3. write 0 under the first digit of dividend then add the first digit with 0.
  4. The result obtained in the second step by adding 0 and the first digit is multiplied with the compliment , the result is written under the second digit and than they undergo addition. Repeat this step up-to last digit of the dividend. If any of the result are of more than one digit than the last digit of resultant is written and others are carries to the previous digit. Note that the result obtained is added to next digit even if it  is more than 1 digit number.
  5. Now if the remainder obtained is the number greater than 9 than that remainder is again divided by 9.
  6. Now repeat step 4 until you get remainder less than 9.  
   Note : as the divisor is of 1 digit, the last digit  is differentiated with a slash , if the divisor is a 2 digit number than last 2 digit should be differentiated   with a slash for the remainder. 

Lets understand with an example 

 275/9


1)  separate the last digit of dividend with a slash for the remainder


2) 0 under first digit : 2 7/5 
                                  0


3)  add 2 and 0 and it gives 2 , write 2 under 7 => 2+7 =9 now write 9 under 5 and add them it gives 14 



4) Now quotient : 29  , Remainder: 14 , here 14 is bigger than 9 so again it is divided by 9.now again divide  14  in two parts  1 / 4  and  adding the first digit with 0 we get 1 now 1 is multiplied with the compliment of 9 that is 1 and added with 4  which gives 5  . Thus it gives 1 = quotient and 5 as remainder as 5 is smaller than 9  its final remainder .

                                         1  /  4
                                     +  0     1    
                                         1  /  5



5) quotient 29 and sub-quotient from above step are added to get the final quotient  , 29 +1 =30 and remainder is 5 



Final quotient is 30 , Remainder : 5

Take another example

                                        9 /  4231159

1)      4 2 3 1 1  5  /  9


2)        4   2  3   1   1   5  /  9
         +
           0  

3)       4   2   3    1   1    5  /  9
        +
          0                                   
       
          4

4) 4     2       3       1        1       5   /  9
       +      +       +       +        +        +
        4        6       9        10     11     16  
   4    6       9      10       11     16      25


5)      4      2        3         1      1        5  /    9
             +        +        +       +       +          +
                 4        6         9      10      11     16  
         4      6        9      1   0   1    1  1  6 /   25
                             +           +        +
                                 
 6)       4    2     3     1     1      5    /    9
              +     +     +    +      +          +
                 4     6      9    10    11      16  
           4   6    1  0   1      2      6     /  25
                   +

7)      AS 25 is greater than 9 it cannot be remainder, so it is again divided by 9 repeating same steps as above. Split 25 into two parts.

               470126 //    2 / 5
                               +
                                   0        
                                   2

8)  Now  as  7 is less than 9 it is the final remainder

              470126 //   2   /    5
                               
                                   +
                                           2        
                                 2    /   7

9)   470126 and 2 are quotients and are added to get the final quotient

         4 7 0 1 2 6   /  2  7
                           +

Final Answer: 470128/7

Quotient :  470128     Remainder :  7


NOTE: If the remainder is equal to 9 then divide it with regular division method.
example: 2340/9

here at last 9 comes as remainder and 259 as the quotient . so divide 9 with 9  that is 9 *1=9 so here weget quotient equals 1 and remainder 0 . Add both quotient 259+1 = 260  and  remainder =0.


similarly, practice some examples and get expertise over it for mental calculation

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