'Number Digit' of a number :-

In Vedic Maths, the Number Digit (ND) of a number is called 'Navasesh' meaning 'nine and its remainder'.

USES AND APPLICATIONS :

This concept is used as a general method of verification in mathematics, to verify various mathematical operations such as addition, subtraction, multiplication and division.
But, before we go ahead, here are some important points to remember :
  • The number digit of any non-zero number is always a single-digit non-zero number (obviously, the number digit of zero is always zero).

  • If number is made up of all 9's and /or all sub-additions of 9's, then its number digit is 9.

  • If you encounter any negative number while applying this verification rule to subtraction, convert it to a positive number, by just adding 9 to the negative number (for ex. if your answer is -4, convert it like this :
    -4 + 9 = 5).

  • While multiplying this verification rule to division, convert the number digit equivalent into a multiplication form and then apply the verification rule.

Note : This method of checking is not a foolproof method, but works reasonably well.



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Examples :

ADDITION :
          2 7 5 9  →  ND  →  5       → 5 + 2 = 7
     +  1 4 8 7  →  ND  →  2
        4 2 4 6  →  ND  →  7
ND's of both sides of the equation are 7. Therefore, the above addition expression is correct.

SUBTRACTION :
          7 3 2 1  →  ND  →  4       → 4 - 7 = -3 (convert to positive number)  →  -3 + 9 = 6
     -  3 4 8 1  →  ND  →  7
        3 8 4 0  →  ND  →  6
ND's of both sides of the equation are 6. Therefore, the above subtraction expression is correct.

MULTIPLICATION :
          4 6 2  →  ND  →  3       → 3 * 3 = 9
     *  1 2 9  →  ND  →  3
  5 9 5 9 8  →  ND  →  9
ND's of both sides of the equation are 9. Therefore, the above multiplication expression is correct.

DIVISION :
          2755956 ÷ 129 = 21364  →  ND (2755956) ÷ ND (129) = ND (21364) 
         ... ND (2755956) = ND (21364) * ND (129)
                  ↓                               ↓            ↓       
            ND (3)             =         ND (7) * ND (3)
                  ↓               =              ↓
                  3               =         ND (21)
                                   ok           
                  3               =             3
ND's of both sides of the equation are 3. Therefore, the above division expression is correct.

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