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Basic Requisites – Basics of Vedic Mathematics

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Vedic Mathematics Vinculum Process

While studying Vedic Mathematics, I came across some of the important concepts which forms base for most of those techniques.

So before actually going through Vedic Mathematics techniques we need understand the basics used. I have  collected all these concepts and named them as Basic Requisites for understanding and learning Vedic Mathematics.

Basics of Vedic Mathematics:

  1. Place Value System
  2. Vinculum Numbers (English Meaning: Complement of a Number).
  3. Work with Quotients & Remainders.

1. Place Value System:

It denotes the value present at particular place. Place Value concept is used for Vinculum Numbers (For conversion of Vinculum Numbers to normal numbers and vice versa).

Example: 2345

  • 5 is present at Units place. Hence Place Value of 5 is 5.
  • 4 is present at Tens place. Hence Place Value of 4 is 40.
  • 3 is present at Hundreds place. Hence Place Value of 3 is 300.
  • 2 is present at Thousands place. Hence Place Value of 2 is 2000.

Hence
2345 = 2000 + 300 + 40 + 5

2. Vinculum Numbers:

Vinculum means bar(line) present over the symbol/digit.

Sanskrit Name:

         विनक्ल्म्

English Translation:

Complement of a number.

 Vinculum Process or Vinculum Numbers are the very basics of Vedic Mathematics.

Vinculum Numbers is concept used in Vedic Mathematics and are those numbers which have atleast 1 digit which is negative (having bar over them). Also called as Bar Numbers.

As seen earlier Normal Number can be written as

2345 = 2000 + 300 + 40 + 5

Similarly Vinculum Numbers can be written as and can be converted to normal numbers as below:

Vedic_Mathematics_Vinculum

Another Approach for converting Vinculum Number to General Number, I generally remember this from     R –> L as below (for better approach watch my below Video “Vedic Mathematics -1 (Vinculum 1of3)”).

  1. Convert 1st Bar digit from Right side to Normal digit (By taking its 10’s complement)
  2. Decrement the previous digit by 1 (If it comes negative then repeat these 2 steps.)

Vedic_Mathematics_Subtraction_Vinculum1

Vinculum (Bar Number)  –>  Normal Number  (Check the video)

R –> L

  1. Find 1st Bar digit, take its 10’s complement.
  2. (a).If next digit is again a Bar digit, take its 9’s complement continue (a) until a non-bar digit is obtained.
    (b). Decrement non-bar digit by 1.
  3. Continue (1) and (2) till complete number is covered.

Usage:

Vinculum numbers are used especially whenever we have higher digits (6, 7, 8, 9) in a number for carrying out Subtraction, Multiplication, Division, etc. Like any other number, Vinculum Number is a hypothetical number used in Vedic Mathematics to make calculations faster.

Check this => Why numbers are Hypothetical.

Similarly normal numbers can be converted to Vinculum (Bar) numbers. (i.e. converting bigger digits like 6,7,8,9 to smaller digits like 1,2,3,4.) (watch below Video “Vedic Mathematics -2 (Vinculum 2of3)”).
Similar process can be followed from R –> L

  1. Convert normal digit in Bar digit (By taking its 10’s complement)
  2. BUT Increment the previous digit by 1.

Let’s take few examples in which we don’t want given number to have any digit greater than 5.

(Convert Greater Digits like 6, 7, 8, 9 to smaller Vinculum Digits like 1, 2, 3, 4  using Vinculum process.)

Normal number –> Vinculum (Bar) number (Check the video)

R –> L

  1. Find 1st digit > 5, take its 10’s complement with a Bar over it.
  2. (a).If next digit is  >= 5, take its 9’s complement with a Bar over it & continue this till a digit < 5 is obtained.
    (b). Increment <5 digit by 1.
  3. Continue (1) and (2) till complete number is covered.

 

Vedic_Mathematics_Subtraction_Vinculum2

Subtraction using Vedic Mathematics:

Most of us have difficulty and uncertainty whenever we need to do subtraction, especially when it comes to subtraction of larger digits from smaller digits.

Vedic Mathematics’s Vinculum process can also be used for Subtracting 2 numbers.  (How ?? watch my below Video “Vedic Mathematics -1 (Vinculum 1of3)”).

Process (R –> L):

  • If bigger digit is to be subtracted from smaller digit, then just perform Bigger digit – Smaller digit and write bar over it.
  • If smaller digit is to be subtracted from bigger digit then carry usual method.
  • In final answer (Vinculum number) convert to normal number using Vinculum process.

Vedic_Mathematics_Subtraction_Vinculum3

Multiplication and Division examples in Vedic Maths which uses Vinculum Process will be seen in respective topics.

Multiplication in Vedic Mathematics using Nikhilam Sutra

Multiplication in Vedic Mathematics using Urdhva Tiryak Sutra

Division in Vedic Mathematics using Paravartya Sutra

Division in Vedic Mathematics using Anurupyena Sutra

Division in Vedic Mathematics using Flag Method

Watch below mathlearners video on Vinculum

3. Quotient and Remainders:

This is another important concept of Vedic Mathematics. We will follow the below formula and the concept that Remainder is ALWAYS < Divisor.

Dividend = Quotient x Divisor + Remainder 

Examples:

33 ÷ 6 = 5/3 … where 5 -> Quotient & 3 -> Remainder
34 ÷ 6 = 5/4 … where 5 -> Quotient & 4 -> Remainder
35 ÷ 6 = 5/5 … where 5 -> Quotient & 5 -> Remainder
36 ÷ 6 = 6/0 … where 6 -> Quotient & 0 -> Remainder

So on observation we can say that the Remainder can never be >= Divisor.

But in Vedic mathematics in some examples depending on some criteria we need to play with Quotients and Remainders i.e. use Remainder >= Divisor for carrying out the process. But the in final answer Remainder can never be >= Divisor.

Thus for carrying out the process above examples (from bottom to top) can also be written as: ( ( watch my below Video “Vedic Mathematics -4 (Playing with Quotients and Remainders)”).)

36 ÷ 6 = 5/6 OR 4/12 OR 3/18 and so on.
35 ÷ 6 = 4/11 OR 3/17 and so on.

And vice versa for calculating final answer(Remainder can never be >= Divisor).

If we obtained Remainder(R) which is >= Divisor(D), we divide R by D and corresponding obtained quotient is added with obtained Q and new remainder becomes our R.
Lets say we obtained Q=4 & R=12, and D used was 11. As R > D, Apply above rule.

So Actuals are Q= 5 and R=1. Q=4 & R=18, and D used was 6. As R > D,

Apply above rule. So Actuals are Q= 7 and R=0.

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Comments

  2. Dear sir,
    Can u mail details of division , i cant understand anything
    so can u send me step by step details of division.

    I have addition, subtraction, multiplication , all these are clear;
    but division section is not clear
    So please i request u, send me step by step details ?

    Thank you,
    Mrs. Jyoti Pawar.

  3. Hi,
    While converting vinculum no. to normal no. following R=>L approach what if the digit after bar digit is a ‘0’

    eg: 1 0 (-6) 6 4 (-6) 0 (-2) 4 ; plz provide solution for this problem.

    • Hello Mamta,

      You can follow same instructions, only it would be more than 1 step to get the answer

      After taking 10’s complement, next non-bar digit needs to be subtracted by 1, hence it will become (-1) and the process to be continued.

      In case of your example
      # 1 0 (-6) 6 4 (-6) 0 (-2) 4
      = 1 0 (-6) 6 4 (-6) (-1) 8 4
      = 1 0 (-6) 6 3 3 9 8 4
      = 1 (-1) 4 6 3 3 9 8 4
      = 0 9 4 6 3 3 9 8 4

      Final Answer: 94633984

      Let me know if this clears you.

  4. I’m 17. I’m a university student, studying Computer science.I heard, of vedi mathematics today when I asked a 9th grade Indian friend of mine, to calculate the remainder of a polynomial equation. He calculated it in seconds, mentally. It took me a couple of minutes, to mentally verify that it’s correct. I want to be able to turn my brain into a scientific calculator, is that possible with Vedi Mathematics?
    If so, direct me to where I can learn it in detail.

    • Yes Lancelot, Vedic Mathematics definitely helps for solving problems in faster ways but it requires lot of practice and understanding.

      You can refer original book of Vedic Mathematics by Tirthji Maharaj or you go through the topics on mathlearners.com in the same sequence as mentioned. Let me know if you come across any doubts.

  5. I’m 17. I’m a university student, studying Computer science.I heard, of vedi mathematics today when I asked a 9th grade Indian friend of mine, to calculate the remainder of a polynomial equation. He calculated it in seconds, mentally. It took me a couple of minutes, to mentally verify that it’s correct. I want to be able to turn my brain into a scientific calculator, is that possible with Vedi Mathematics?
    If so, direct me to where I can learn it in detail.

    • Hello Sasiraj,

      No sutra is named for Playing with Quotients with Remainders neither it was originally named as it. I categorized it as ‘Playing with Quotients with Remainders’ as the concept is widely used in Vedic Math.

  7. I am still doubtfull about the video of “playing with Remainders and Quotients” …
    in example of D=13,Q=14 and R=11, final ans was 12|37 whereas if we count on the method that u applied in 18/4 example the ans of that example(in D=13,Q=14 and R=11 ) would be
    ((14 x 2)+11)=39….so final ans is 12|39 accordingly…so will you pls clarify on this matter? …..Thanks

    • Nopes Sawan, I have applied the formula
      Dividend = Quotient x Divisor + Remainder

      In case of D=13,Q=14 and R=11:
      When I say 1 quotient goes to Remainder side then
      RHS (Remainder) = 1 x 13 + 11 = 24

      So now D = 13, Q = 13 and R = 24
      Again when 1 quotient goes to Remainder side then
      RHS (Remainder) = 1 x 13 + 24 = 37

      SO Now Q = 12 and R = 37.

      Hope this clears now.

  9. in subraction .when doing: 11111-9876 we get : 18765 with bar on 8765 …. as per rule then bar above 8 .so we should subract 1-1 on the next digit …is that correct what i understood.

  10. Check the following lines from “Quotient and Remainders”, Probably you mistyped in the following lines.

    If we obtained Remainder(R) which is >= Divisor(D), we divide R(not D) by D(not R) and corresponding obtained quotient is added with obtained Q and new remainder becomes R.

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