Vedic Maths Division

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Dear All,             

        Enumerated below are some of the Vedic Mathematics division methods:-

1. Direct Flag Method:-

We have,

1. Divisor - like advisor the number dividing.
2. Dividend - the number being divided. 
3. The Flag - the multiplier.
                     Now, we simply follow the MSD rule. Multiply, subtract and divide.
     In this method we divide with only one digit and use the rest as flag. The Dividend is split for as many digits as the flag. Here if we have one digit in the flag we split the dividend from the right by one digit. The answer after the colon are decimals.
 
      459/83
 
        8    3 )     4     5   :   9       0        0    0              Gross Dividend
                            4        5       4        1     1              Remainder
                              
                             - 0     -15     -15    -9    0              Subtractor
 
                        0   45      44     25       1    10            Net Dividend.     
                  -------------------------------------------------
                        0     5       5        3        0    1             Quotient.

The final answer is 5.5301.

        The system is beautiful and accurate.  Here we can see, 8 is the divisor and 3 is the flag. The whole division is carried by 8 alone. 8 is bigger than 4, so we put 0 and carry forward to get 45. The quotient 0 is multiplied by flag zero to get 0 as the subtractor. Now, 45-0=45. We divide 45 by 8 to get 5 as quotient and carry forward 5 to get 59. The 5 quotient is multiplied by flag 3 to get -15. So, 59-15=44. Now divide this 44 by 8 to get 5 as quotient and carry forward the remaining 4. Now, quotient 5 is multiplied by 3 to get Sub-tractor -15. 40-15=25. This 25 is divided by 8 and so on...

          4852 / 68
     
      6    8   )     4     8       5   :    2        0     0     0         Gross Dividend
                                     6        3        6     6      8           Remainder
                              
                                    -56       -8      -24    -40  -16       Subractor
 
                        0     0      9      24      36      20    64      Net Dividend.     
                  ---------------------------------------------------------
                        0     7      1        3        5      2       9       Quotient.

The final answer is 71.13529
 
Please note the Net Dividend is to be maintained positive. If it becomes negative, go back, reduce the quotient by 1, then multiply quotient by the flag, then subtract and get a positive Net Dividend.
 
 
         85270 / 734
         
   7   3    4 )     8     5       2   :    7        0      0      0           Gross Dividend
                            1       5        3        8      4      8             Remainder
                              
                            -3       -7     -22      -27   -25    -31         Subractor
 
                             12    45      15       53    15     49          Net Dividend.     
                  ------------------------------------------------------------
                        1    1      6       1         7       1      6            Quotient.
 
The final answer is 116.1716
The only thing here is the multiplier. The flag 3 & 4 multiplies crosswise with the quotient to get the subtractor.

3  x  4
1       6         The subtractor is 1*4+6*3 = 4+18 = 22 
 
This system is quite effortless. Practice makes one perfect. And the better practice is evidently on PC or mobile.
Urdhava Tirthabhyam { Vertically and Crosswise is widely applied in division. And it makes this  very easy }.

    674255 / 3452
     
3   4   5   2 )     6     7       4   :     2        5      5      0           Gross Dividend
                             3       6         8        6      4      3             Remainder
                              
                             -4      -41      -67     -55   -33    -28         Subractor
 
                             33     23       15       10    12     2          Net Dividend.     
                  ------------------------------------------------------------
                        1    9       5          3       2       3      0            Quotient.
 
 
 The final answer is 195.3230

4    5     2
1    9     5        Here the ends are cross multiplied and the center is vertical.
                       4*5+2*1+5*9 = 67. This is our subtractor.
 
Hope you have enjoyed this small discourse. We read it way back about 18 to 20 years ago. Evidently Vedic Maths is fantastic, magnificent, vast and praise worthy.
 
2. Nikhlam Sutra ( all from 9 last from 10 ).
 
23/9 = ?,  quotient 2, remainder 2+3=5
254/9=?,     q = 25, rem = 25+4=29, final q = 25+3=28, rem=2.
456/99 = ?, q = 4, rem= 4+56=60
 
And so on. split the dividend according to the number of 9's. The left of the split is the quotient. Right side is the remainder but is carried forward if greater than the quotient. 
 
3258/9
                3    2    5  :  8
                0    3    5      10 
            -------------   
                3    5    10    18 
starting from right removing 9's 
3 5 12 0    3 6 3 0  so the final quotient is 363 remainder 0.
{ Please observe that 9 = 1/ -1 or 9 bar 1. So, we put 1 as divisor and -1 as flag.
When we multiply the quotient by -1 to get the subtractor it actually becomes an adder. This is directly applied out here. }
 
Divide 12123 by 879
 
879 is close to base 1000. If we write 879  as 1 -1 -2 -1. It means 1000 - 121. we use Nikhlam Sutra to arrive at 121 1  would be the divisor and the rest flag. As the flag is negative it multiplying result would be added.
 
                 879   )  1    2  :  1    2    3                79 )    1  :  0    5
                 121            1     2    1                    21             2    1   
                                          3    6    3                       ---------------------             
                            ___________________                         1     2    6
                              1   3     6    9    6
                13 quot, 696 rem.                             1  quot, 26 rem.
 
                               
3. Parvartya Sutra  ( transpose and adjust )
 
     Divisor just greater than 10, 100, 1000, ....
                
    23689  / 112                                          13445 / 121                     
    
        1 1 2 ) 2   3   6 :  8    9                       1 2 1  )    1    3    4   :  4    5       
                        -2  -4                                                       -2    -1   
                             -1   -2                                                        -2    -1    
                                    -1   -2                                                        -2    -1    
                  -----------------------                                   ------------------------------------
                    2   1    1 :   5   7                                      1    1    1   :   1    4          
                Q = 211, rem = 57                                  Q = 111 , rem = 114

        1 becomes the divisor and the rest flag. From the right the decimal point is taken same as the number of digits in the flag. We continue the procedure until the last digit of the Dividend is reached. 
   
There are other methods like Ekadhikena Purvena, Anurupyena Sutra which are derivatives of some of the above. Planning to discuss in future articles.

Kind Regards,
Jeeves.


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