Multiplication

Sutra : " Nikhilam Navatashcharamam Dashataha "

Meaning : All from 9 and the last from 10.



Upasutra : "Aanurupyena "

Meaning : Proportionately



This simple sutra teaches us to do multiplication of numbers which are close to a BASE or Aadhara such as 10, 100, 1000, 10000 etc.





Consider the example given below

8 * 13



Step 1 : Since 8 and 13 are close to 10 we shall consider 10 as the base.



8 - 10 gives -2 and

13 - 10 gives +3



Step 2 : Write the problem as below



8 -2

13 +3



Step 3 : For the first part of the answer add diagonally.

i.e. 8 + 3 Or 13 - 2 == 11



Write it as 8 -2

13 +3

11 0

( One '0' is added because the base is 101)



Step 4 : For the second part multiply the number in the RHS column and put it below zero and total to obtain the final answer.



8 -2

13 +3

11 0

-6

10 4



Hence the Answer is 104.





Example 2 :



Consider 945 * 1005



Here the base can be considered to be 1000

Therefore the problem is written as



945 -055

1005 +005



By Diagonal Addition

945 + 005 == 1005 - 055 == 950



945 -055

1005 +005

950 000

By linear multiplication of RHS

-55 * 5 = -275



945 -055

1005 +005

950 000

-275

949 725



Hence the answer is 949725



Aanurupyena



An Upasutra or Sub Formula of Nikhilam is Aanurupyena which means 'Proportionately'.



Here we consider multiples and sub-multiples of the Main Base as the Working Base.



Consider 53 * 57

Let us consider the working base to be 50, which is a sub multiple of the main base 100.



Let 'x' be (Main Base) / (Working Base)



Here x = 100/50 = 2

Write the numbers as in normal Nikhilam



53 +3

57 +7

60 00

(Two '0' s are added here as the Main Base is 100)



Now divide the first answer by x , here 2



53 +3

57 +7

30 00

Now do the second part as in normal method



53 +3

57 +7

30 00

+21

30 21



Hence the Answer is 3021.

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Navasesh

Navasesh is a general method of verification formulated in Vedic mathematics. This can be used to verify various mathematical operations such as Addition, Subtraction, Multiplication etc.

Navasesh means ' nine and its remainder '.
Examples :
Navasesh of 23 ---> N(23) == N(2+3) == N(5) == 5
Navasesh of 82 ---> N(82) == N(8+2) == N(10) == N(1+0) == N(1) == 1
Navasesh of 49 ---> N(49) == N(4+9) == N(13) == N(1+3) == N(4) ==4
Navasesh of 105 ---> N(105) == N(1+0+5) == N(6) == 6

Addition
We know that 23 + 82 = 105
To verify :
N(23) + N(82) = N(5) + N(1) == N(5+1) == N(6) == 6
N(105) = N(6) == 6
Hence N(23) + N(82) = N(105)

Subtraction
We Know that 82 - 49 = 33
To verify :
N(82) - N(49) = N(1) - N(4) = N(1-4) == N(-3) == N(9-3) == N(6) == 6
( Note that -3 here has been converted to 9-3 such that negative number is eliminated)
N(33) = N(3+3) == N(6) == 6
Hence N(82) - N(49) = N(33)

Multiplication
We know that 23 * 49 = 1127
To verify :
N(23) * N(49) = N(5) * N(4) ==N(5 * 4) ==N(20) = N(2) =2
N(1127) = N(1+1+2+7) = N(11) = N(2) =2
Hence N(23) * N(49) = N(1127)

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The Magic of Vedic Maths

What is Vedic Math?


What does mathematics have to do with Hinduism? Well, just as the basic principles of Hinduism lie in the Vedas, so do the roots of mathematics. The Vedas, written around 1500-900 BCE, are ancient Indian texts containing a record of human experience and knowledge. Thousands of years ago, Vedic mathematicians authored various theses and dissertations on mathematics. It is now commonly believed and widely accepted that these treatises laid down the foundations of algebra, algorithm, square roots, cube roots, various methods of calculation, and the concept of zero.
Vedic Mathematics
"Vedic Mathematics" is the name given to the ancient system of mathematics, or, to be precise, a unique technique of calculations based on simple rules and principles, with which any mathematical problem — be it arithmetic, algebra, geometry or trigonometry — can be solved, hold your breath, orally!

Sutras: Natural Formulae
The system is based on 16 Vedic sutras or aphorisms, which are actually word-formulae describing natural ways of solving a whole range of mathematical problems. Some examples of sutras are "By one more than the one before", "All from 9 & the last from 10", and "Vertically & Crosswise". These 16 one-line formulae originally written in Sanskrit, which can be easily memorized, enables one to solve long mathematical problems quickly.

A Simple & Easy System
Practitioners of this striking method of mathematical problem-solving opine that Vedic maths is far more systematic, coherent and unified than the conventional system. It is a mental tool for calculation that encourages the development and use of intuition and innovation, while giving the student a lot of flexibility, fun and satisfaction. Therefore, it's direct and easy to implement in schools — a reason behind its enormous popularity among educationists and academicians.


Try These Out!
· If you want to find the square of 45, you can employ the Ekadhikena Purvena sutra ("By one more than the one before"). The rule says since the first digit is 4 and the second one is 5, you will first have to multiply 4 (4 +1), that is 4 X 5, which is equal to 20 and then multiply 5 with 5, which is 25. Viola! The answer is 2025. Now, you can employ this method to multiply all numbers ending with 5.
· If you want to subtract 4679 from 10000, you can easily apply the Nikhilam Navatashcaramam Dashatah sutra ("All from 9 and the last from 10"). Each figure in 4679 is subtracted from 9 and the last figure is subtracted from 10, yielding 5321. Similarly, other sutras lay down such simple rules of calculation.

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