Division by a Number  Ending with 9

             This concept is a real gem of Vedic Maths .After learning this concept you experience lot of thrill in yourself .It  is
             very easy and you can find it very useful for your calculations
                Denominator ending with 9

            Let our question  is divide 259 by 19 up to 6 places   of decimals

            First we solve it by conventional method
                            
                                 13.631578
                           19)  259
                                   19
                                     69
                                     57
                                     120
                                     114
                                         60
                                         57
                                           30
                                           19
                                             110
                                               95
                                               150
                                               133
                                                  170
                                                   152
                                                       18

                                   I think all are well conversant  in this  method, so  no need  to explain further .
                                   Now we learn the division of 19 by Vedic  method

                                                259=????
                                                 19
                                   Steps     259   =    25.59       Put  proper decimals and  make 19 to20 ,take next number ie
                                                  19            2            19 to 20 ,29 to30 , 39 to 40 119 to 120 etc etc
                                                         

                                                      Now it is much easier to divide by 2 in comparision of 19  or 3 to 29 or 4to 39
                                                      Now we learn  steps
                                                             1
                                                          2 59           First we divide  2 by 2  1 is Quotient no Remainder

                                                                                13
                                                          2 59       Now add 1 to 5  ,6 is our gross  so divide 6 by 2, 3 is Quotient, no Remainder
                                                                                 

                                                             13 6
                                                          2 59       Now add 3 to 9  ,    ie 12 is now our gross   so divide 12 by 2    6is Quotient
                                                                                                and  no remainder                                                                                              
                                                                                             

                                                             13 63
                                                          2 59       Now nothing to remain in  our main number  ie259  so take 6  directl
                                                                        now  6  become  our gross   so divide 6 by 2    3is Quotient  No remainder
                                                                      

                                                                                13 631
                                                          2 59       Take 3  directly , now  3 become our gross   so divide 3 by 2  1 is   Quotient   
                                                                                           1     1  remainder
                                                                    
                                                                                                                                                                                                                                                             
                                                                                    13 6315
                                                          2 59               Take Quotient 1   put it before remainder 1 ,it looks like 11 ,now 11
                                                                         11     become  our gross   so divide 11 by 2    5 is   Quotient   1 remainder

                                                                 
                                                                                 13 63157
                                                          2 59               Take Quotient 5   put it before remainder 1 ,it looks like 15 ,now 15
                                                                         15   become  our gross   so divide 15 by 2    7is   Quotient   1 remainder                
                                                         

                                                                         
                                                                                 13 631578
                                                          2 59               Take Quotient 7   put it before remainder 1 ,it looks like 17 ,now 17
                                                                          1   become  our gross   so divide 17 by 2    8is   Quotient   no remainder        
       
                                                                               Repeat the above steps if you want to find the values further.

                                                                       Now our answer  after proper decimal  is 13.631578

                                                            Now check both answers   whether two answers are same ??????

                                                                           Let us see one more example  392  =?      Make denominator 29  to 30
                                                                                                            29

                                                                                             392
                                                                                              30
 

                                                                                                     1    3 5 1 724
                                                                                            =   3  9    2                                                /3
                                                                                                    10 ,15 ,5,21,7,12

                                                                                                  
                                                                                           =   13.51724  Answer
                                                                                              

                                                   See one more example           485
                                                                                                 39

                                                                                                485    =   48.5
                                                                                                 4 0           4
                                                                                                                    

                                                                                                   1  2   4    3     5
                                                                                                 48  5                                                 /4
                                                                                                   9 17  14  23  53

                                                                                                  =   12.435  Answer

                                               Now see one example of carry      297    =    297  =     29.7
                                                                                                     29            30             3
                                                                                                      

                                                                                                  9 12   4   1  3     =102413
                                                                                            2 9 7                                                      /3
                                                                                                   2                     when we add 16 to  2 consider it 20     
                                                                                                   16             not  2 , it is why 2(20)+16 =36. Eliminate
                                                                                                    36   12 4  11   1of 12  consider 1 as carry ,1
                                                                                                                                  add to 9 , become 10
                                                                                       Now answer is 10.2413

                                           Let us see one example of 3 digit          3469     =  3469  =  346.9
                                                                                                        129          130          13

                                                                                                    
                                                                                                           2   6   8     9      1
                                                                                                       346   9                                       /13
                                                                                                           88 10        consider its 100 not 10
                                                                                                                15
                                                                                                                115  118   19

                                                                                                      =   26.891   Answer

                                                                                                 

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