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Last Two Classes
     Vedic Mathematics




                                               
                                                  We learnt how to multiply using two sutras
                                                  namely ekhadhikena Purvena and Nikhilam

M. Krishnamoorthy (moorthy)                  In particular, you know what the answers for
email address: moorthy@cs.rpi.edu            39 * 31, 48 * 42, 78 * 82, 6 45 * 6 55
URL:                                         (using ekadhikena sutra) and
http://www.cs.rpi.edu/~moorthy/vm
                                             53 * 52 , 89 * 92, 104 * 122 (using nikhilam
                                               method).




        Outline of this class                                     Sutra




 ¡
  How to compute decimal expansions of       1. Ekadhikena Purvena
  1/19, 1/29, …1/89 etc using Ekadhikena     By one more than the previous one.
  Purvena                                    The preposition “by” means the operations




 ¡
  Division Using two sutras using nikhilam    this sutra concerns are either multiplication
  and urdhva-tiryagbhyam .                    or division ( In the case of
How to divide 111 by 89 1234 by 888,          addition/subtraction preposition to/from is
16384 by 128.                                 used.). In this case it is useful for both of
                                              them.
Examples               What is the method?
1/ 19 =                      Two methods: division and multiplication:
                             Multiplication: Start with 1 as the last digit.
                                               1
1/29 =                       Multiply the last digit by 2 (I.e., one more
                              than 1 (1 being the first digit in 19) and that
                              is the previous digit.             21
                             Repeat the previous step: 421
                             Continuing                 68421
                                                       1




           Crucial steps!!                    Continue
               6 8 4 21       1/19=. 0 5 2 6 3 1 5 7 8 9 4 7 3 6 8 4 2 1
               1               1/29=
Multiply 6 by 2 and add 1.     .0 3 4 4 8 2 7 5 8 6 2 0 6 8
                 368421         9 6 5 5 1 7 2 41 3 79 3 1
                11
Continuing we get            1/39=
           47368421
          1 11
Method 2                                       Continuing
Division Method for computing 1/19               1/19=
Divide 1 by 2 ( one more than 1 in 1 in 19).     .0 5 2 6 3 1 5 7 8 9 4 7 3 6 8 4 2 1
  Place the quotient in line 1 and reminder in   1/29=
  line 2                                         .034482758620689655172413
  05 2                                             7931
1    1
Treat the last reminder quotient as one
  number and divide by 2 and repeat.




                Divisions                                  More Examples
Nikhilam Method:                                 What is the quotient and reminder when
Examples:                                         12031 is divided by 9?
12 / 9 = 1 2                                        12031
              1                                       1336
            1 | 3 Quotient : 1 Reminder: 3       Quotient is 1 3 3 6 Reminder 7
 53/9     =      53
                   5 Quotient: 5 Reminder 8
More Examples                 Examples
1 8 over 9                   1011649 divided by 9
225 over 9
                             111/89
136 over 9
                             1234 / 888
237 over 9
                             111/73

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Vm3

  • 1. Last Two Classes Vedic Mathematics   We learnt how to multiply using two sutras namely ekhadhikena Purvena and Nikhilam M. Krishnamoorthy (moorthy) In particular, you know what the answers for email address: moorthy@cs.rpi.edu 39 * 31, 48 * 42, 78 * 82, 6 45 * 6 55 URL: (using ekadhikena sutra) and http://www.cs.rpi.edu/~moorthy/vm 53 * 52 , 89 * 92, 104 * 122 (using nikhilam method). Outline of this class Sutra ¡ How to compute decimal expansions of 1. Ekadhikena Purvena 1/19, 1/29, …1/89 etc using Ekadhikena By one more than the previous one. Purvena The preposition “by” means the operations ¡ Division Using two sutras using nikhilam this sutra concerns are either multiplication and urdhva-tiryagbhyam . or division ( In the case of How to divide 111 by 89 1234 by 888, addition/subtraction preposition to/from is 16384 by 128. used.). In this case it is useful for both of them.
  • 2. Examples What is the method? 1/ 19 = Two methods: division and multiplication: Multiplication: Start with 1 as the last digit. 1 1/29 = Multiply the last digit by 2 (I.e., one more than 1 (1 being the first digit in 19) and that is the previous digit. 21 Repeat the previous step: 421 Continuing 68421 1 Crucial steps!! Continue 6 8 4 21 1/19=. 0 5 2 6 3 1 5 7 8 9 4 7 3 6 8 4 2 1 1 1/29= Multiply 6 by 2 and add 1. .0 3 4 4 8 2 7 5 8 6 2 0 6 8 368421 9 6 5 5 1 7 2 41 3 79 3 1 11 Continuing we get 1/39= 47368421 1 11
  • 3. Method 2 Continuing Division Method for computing 1/19 1/19= Divide 1 by 2 ( one more than 1 in 1 in 19). .0 5 2 6 3 1 5 7 8 9 4 7 3 6 8 4 2 1 Place the quotient in line 1 and reminder in 1/29= line 2 .034482758620689655172413 05 2 7931 1 1 Treat the last reminder quotient as one number and divide by 2 and repeat. Divisions More Examples Nikhilam Method: What is the quotient and reminder when Examples: 12031 is divided by 9? 12 / 9 = 1 2 12031 1 1336 1 | 3 Quotient : 1 Reminder: 3 Quotient is 1 3 3 6 Reminder 7 53/9 = 53 5 Quotient: 5 Reminder 8
  • 4. More Examples Examples 1 8 over 9 1011649 divided by 9 225 over 9 111/89 136 over 9 1234 / 888 237 over 9 111/73