Like Multiplication, Tirthaji Maharaj has classified tricks to Divide Numbers in Vedic Mathematics in Specific and General Methods. Specific Division Methods can be applied when numbers satisfy certain conditions like Divisor slightly less than 100 or Divisor slightly greater than power of 10 or Divisor is ending with 9, etc. While General Multiplication Methods can be applied to any types of numbers.
Depending of Divisor and Dividend, Division in Vedic Mathematics are classified in the form of Sutras as below. Lets see the Vedic Mathematics Division techniques:
Nikhilam Sutra (Specific Technique)
Paravartya Sutra (Specific Technique)
Anurupyena Sutra (Specific Technique)
Direct Flag Method (General Technique)
Ekadhikena Purvena (Specific Technique)
Vestanas (General Technique)
Nihilam Sutra is a Specific Method to Divide Numbers using Vedic Mathematics. This Vedic Maths Division Method can be applied when Divisor is closer to power of 10 BUT less than that of it.
Using Nikhilam Sutra, you can easily divide when divisor is like 98, 92, 995, 89997, etc.
Lets see division math tricks using Nikhilam Sutra. Example: 243/9
9 is 1(deficiency) less than 10(nearest power of 10). (that 1 is written in white color below divisor in example)
Split Dividend in 2 parts (Quotient & Remainder) in such a way Remainder to have same number of digits as that of Divisor. In this case its 1 digit.
Take 1st digit – 2 down as it is.
Multiply the above deficiency (1) with the 2 and put below 4 and add them column wise to get 6.
Multiply deficiency (1) by 6 and put below 3 and add column wise to get 9.
As last column is filled, we stop the process.
We know the concept that Remainder can NEVER be >= Divisor,� as Remainder 9 is = our Divisor 9, we divide 9 by 9 to get Quotient 1 and Remainder as 0.
Add the Quotient 1 to original Quotient 26 to get 27.
Direct Division (Flag Method) is a general method of Division in Vedic Mathematics shows shortcut to divide any types of numbers. It is a shortcut method for division of large numbers.
Single Digit Flag
1234/12 –� Dividend = 1234 and Divisor = 12. Split divisor (12) in 2 parts (1 and 2) where division will be carried using ONLY 1(new divisor) and 2 is called as flag. As flag is single digit, Split dividend in 2 parts such that 2nd part will have same number as that of flag i.e. 1 digit.
Process (see the example for each step):
Division of 1 by 1 (Q=1 and R= 0). Write Q=1 and carry forward the R=0(written in white under and between 1&2).
Multiply the new Q(1) with the flag(2) and subtract this product from 02 = 0 and divide this subtraction by 1. It gives Q= 0 and R= 0(Carry forward R=0). (i.e. Multiply, Subtract, Divide)
Follow same above process, So multiply new Q(0) with flag(2) and subtract this product from 03 = 3 and divide this subtraction by 1. It gives Q= 3 and R= 0(Carry forward R=0).
For remainder we carry same process EXCEPT we don’t divide. (i.e. Multiply, Subtract) So multiply new Q(3) with flag(2) and subtract this product from 04 = -2. As we get negative subtraction, we reduce the quotient by 1 and increase the remainder by the 1st multiplier of new multiplier (1X1 =1). So new Q = 2 and new R =1. (Refer Topic Work with Quotient and Remainder). We carry this method till we don’t have negative subtraction.
Now Multiply the new Q(2) with the flag(2) and subtract this product from 14 = 10(positive) and put it down as it is.
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