VEDIC MATHEMATICS FOR BEGINNERS

Lesson 3

1. On dividing 1, the digit in the numerator by 2, we get the quotient 0 and remainder 1.
   
   We write
                .0 quotient
                    1 remainder

2. Now combine the digits formed by the remainder and quotient, i.e., 10 and divide it by 2. we get quotient 5 and remainder 0. We write
   
   ₁05

3. Dividing 5 by 2, the quotient is 2 and remainder 1, we write
   
   ₁05₁2

4. Combining remainder 1 and quotient 2, we get 12. Dividing 12 by 2. We get quotient 6, and remainder 0. We write
   
   ₁05₁26

5. Next dividend is 6, we got  ₁05₁263

6. Next dividend is 3, we get   ₁05₁263₁1

7. Next, we get dividend 11, quotient 5 and remainder 1
   
   ₁05₁263₁1

8. Next, dividend is 15, quotient 7 and remainder 1, we get
   
   ₁05₁263₁1₁5

9. Continuing this process, we get 1 as 18th quotient and 0 as remainder, i.e.,
   
   ₁05₁263₁1₁5₁7₁89₁47₁3₁68421
   
   But this is exactly the same as what we began with. this indicates that the digits will repeat at this place, hence, we stop the division process. Thus
   
   1/19  = 0.052631578947368421

10. After a little practice, the single step procedure will work as
    
    1/19  = .₁05₁263₁1₁5₁7₁89₁47₁3₁68421

11. The procedure can be further shortened to its half. Let us put down the first 9 digits in one row and the remain in 9 digits in the second row and add the two rows, i.e.,
    
      0 5 2 6 3 1 5 7 8
    +9 4 7 3 6 8 4 2 1
    _______________
      9 9 9 9 9 9 9 9 9
    
    Thus, when half the work is completed (i.e., up to 9 digits in this case), the remaining digits can be obtained by subtracting each of the digits, already obtained, form 9 (i.e., complement of 9 ) A question arises - How do we know that half of the number of digits have been obtained? The answer is : as soon as we reach the quotient as "the difference between the numerator and denominator of the original fraction, i.e., 19 - 1 = 18, we shall have completed exactly half the work. We stop the process of division and we write the complements from 9 of each of the digits starting from the first digit, i.e.,
    
    ₁05₁263₁1₁5₁7₁8   /  947368421
    
               19 - 1  = 18      Complements from 9

Note: This project is given with a view to appreciate and enjoy our age old Vedic Mathematics. The interested students should refer to the book "Vedic Mathematics" written by Sri Bharti Krisna Tirthaji. The students may also log on to the following website to learn VedicMathematics containing lessons on Vedic Mathematics in a simplified manner (even students of class III onwards can understand them well)

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