Sci-TECH-Up to date: Vedic Mathematics

Vedic Mathematics is the ancient methodology of Indian mathematics which has a unique technique of calculations based on 16 Sutras (Formulae). It covers explanation of several modern mathematical terms including arithmetic, geometry (plane, co- ordinate), trigonometry, quadratic equations, factorization and even calculus. It contains a list mental calculation techniques claimed to be based on the ancient Vedas. It’s a unique technique of calculation based on simple principle and rules with which any mathematical problems like arithmetic, algebra, trigonometry or geometry can be easily solved. Vedic Mathematics sharpens your mind, increase mental ability, and intelligence.

The system uses sixteen word formula e which relate to the way in which we use our mind.

The 16 sutras are as follows

#	Name	Meaning
1	Ekadhikena Purvena	By one more than the previous one
2	Nikhilam Navatashcaramam Dashatah	All from 9 and the last from 10
3	Urdhva-Tiryagbyham	Vertically and crosswise
4	Paraavartya Yojayet	Transpose and adjust
5	Shunyam Saamyasamuccaye	When the sum is the same that sum is zero
6	Anurupye Shunyamanyat	If one is in ratio, the other is zero
7	Sankalana-vyavakalanabhyam	By addition and by subtraction
8	Puranapuranabyham	By the completion or non-completion
9	Chalana-Kalanabyham	Differences and Similarities
10	Yaavadunam	Whatever the extent of its deficiency
11	Vyashtisamanstih	Part and Whole
12	Shesanyankena Charamena	The remainders by the last digit
13	Sopaantyadvayamantyam	The ultimate and twice the penultimate
14	Ekanyunena Purvena	By one less than the previous one
15	Gunitasamuchyah	The product of the sum is equal to the sum of the product
16	Gunakasamuchyah	The factors of the sum is equal to the sum of the factors

Imagine how easy, interesting and fun math would be when you will be able to do any calculation in a matter of seconds and solve Math questions in no time. Not only your friends, classmates and teachers will be awe impressed with you but you yourself be proud of your own Mathematical ability.

Ekadhikena Purvena

One More than the Previous is a sutra useful in finding squares of numbers (like 25x25, 95x95, 105x105, 992x992 etc) and special divisions like 1 divided by 19, 29, 39, …. 199 etc. just in one step.

Division

To divide 1 by numbers ending with 9 like 1 divided by 19, 29, 39, ….. 119 etc. is a tedious work, using conventional method. Some of these numbers like 19, 29, and 59 are prime numbers and so cannot be factorized and division becomes all the more difficult and runs into many pages in the present conventional method and the chances of making mistakes are many.

Method 1

For example, take 1/19.In the divisor(19), previous one or the number before 9 is 1. By sutra,Ekaadhika or by adding 1 more to the previous one, we get 2. Lets call the previous one+1 (here 2) as "x".In this method,we start from the end.There will be (divisor-1) terms in the answer.Now,

· Assign last number to be 1.Now,multiply it with "x".ie,

2 1

(1*x)|1

· Now go on multiplying with "x" for (divisor-1)/2 times (here,) [(19-1)/2],ie,

Result: 9 4 7 3 6 8 4 2 1

Process :(2*x+1)|(7*x)|(3*x+1)|[6*x+1

(Carry of last multiplication)]| (8*x)|(4*x)|(2*x)|(1*x)

· In the next step, write the compliment of 9 from the last number onwards,(divisor-1)/2 times

Result : 0 5 2 6 3 1 5 7 8 9 4 7 3 6 8 4 2 1

Process : (9-i)|(9-h)|(9-g)|(9-f)|(9-e)|(9-d)|(9-c)|(9-b)|(9-a)|i|h|g|f|e|d|c|b|a

· Now, prefix 0., and this is your final answer, more accurate than a value that your calculator or computer can give.

= 0.0 5 2 6 3 1 5 7 8 9 4 7 3 6 8 4 2 1

So.try this yourself these 1/29,1/39,1/49.1/59.can also be found in seconds,

For example,

1/29 = 0.0 3 4 4 8 2 7 5 8 6 2 0 6 8 9 6 5 5 1 7 2 4 1 3 7 9 3 1

Multiplication Method: Value of 1 / 19

First we recognize the last digit of the denominator of the type 1 / 9. Here the last digit is 9. For a fraction of the form in whose denominator 9 is the last digit, we take the case of 1 / 19 as follows: For 1 / 19, 'previous' of 19 is 1. And one more than of it is 1 + 1 = 2. Therefore 2 is the multiplier for the conversion.

We write the last digit in the numerator as 1 and follow the steps leftwards.

Step. 1 : 1

Step. 2 : 21(multiply 1 by 2, put to left)

Step. 3 : 421(multiply 2 by 2, put to left)

Step. 4 : 8421(multiply 4 by 2, put to left)

Step. 5 : 168421 (multiply 8 by 2=16, 1 carried over, 6 put to left)

Step. 6 : 1368421 ( 6 X 2 =12,+1 = 13, 1 carried over, 3 put to left )

Step. 7 : 7368421 ( 3 X 2, = 6 +1 = 7, put to left)

Step. 8 : 147368421 (as in the same process)

Step. 9 : 947368421 ( Do – continue to step 18)

Step. 10 : 18947368421

Step. 11 : 178947368421

Step. 12 : 1578947368421

Step. 13 : 11578947368421

Step. 14 : 31578947368421

Step. 15 : 631578947368421

Step. 16 : 12631578947368421

Step. 17 : 52631578947368421

Step. 18 : 1052631578947368421

Now from step 18 onward the same numbers and order towards left continue.

Thus 1 / 19 = 0.052631578947368421'

Method 2

Using the same method, we can find,1/7 and 1/39 etc.

Viz,

1/7 = (7/7) * (1/7) =7*(1/49) , where can be find out by above method.

Also,1/13 = (3/3)*(1/13) =3*(1/39).

Nikhilam Navatashcaramam Dashatah

ALL FROM 9 AND THE LAST FROM 10

Use the formula all from 9 and the last from 10, to perform instant subtractions.

For example 1000 - 357 = ? (subtraction from 1000)

We simply take each figure in 357 from 9 and the last figure from 10.

Step 1. 9-3 = 6

Step 2. 9-5 = 4

Step 3. 10-7 = 3

So the answer is 1000 - 357 = 643

And that's all there is to it!

This always works for subtractions from numbers consisting of a 1 followed by nougats: 100; 1000; 10,000 etc.

Similarly 10,000 - 1049 = 8951

Urdhva-Tiryagbyham

Vertically and clock wise:

Suppose you need 7*6

8 is 3 below 10 and 6 is 4 below 10.

Subtract (10-8)=2............................... step -1 8 2

Subtract (10-6)= 4.............................. step -2 6 4

Subtract (8-4) or (6-2) [crosswise] = 4...... step -3 4 8

Multiply (2*4) = 8................................. step -4

Combine step 3 and 4

So Answer = 48

98*97

Subtract (100-98)=2..................step-1

Subtract (100-97)=3...................step-2

Subtract (97-2)=95....................step-3

Multiply (2*3) =06.....................step-4

Combine step 3 and 4

So Answer =9506

Example -1

Example-2

Example-3

You can get more information here......

Multiplication with a series of 9s

Multiplications with numbers like 9, or 99, or 999, or 9999.....so on. It feels like if multiplier is a big number, the calculation will be tough. But, with the help of vedic math formulae, the multiplication is much easier for all '9' digits multiplier. By using the method given below, we can multiply any number with 99,999,9999, etc. very quickly.

Please note that the methods or the vedic formulae, that we use in this calculation, are "By one less than the one before" and "All from 9 and the last from10".

There are three cases for the multiplication of numbers with a series of 9's.

· Case 1: Multiplying a number with a multiplier having equal number of 9’s digits (like 587 x 999)

Try these

· Case 2: Multiplying a number with a multiplier having more number of 9’s digits (like 4678 x 999999)
· Case 3: Multiplying a number with a multiplier having lesser number of 9’s digits (like 1628 x 99)

The method to solve 'Case 1' and 'Case 2' is the same, but for 'Case 3', the method is different. Let us start with 'Case 1'.

Multiplying a number with a multiplier having equal number of 9’s digits

Multiply 587 by 999

         587
       x 999
       ------------
        586 413

Solution is,

· Let us first do the calculation by conventional method to understand the solution. Result will be 586413.

· Split the answer in two parts i.e. '586' and '413'.

· Let's see the first part of the result, i.e. 586. It is reduced by 1 from the number being multiplied i.e. 587 - 1 = 586. {Vedic sutra "By one less than the onebefore"}

· Now see the last part, i.e. 413. Subtract the multiplicand i.e. 587 from 1000 (multiplier + 1). Vedic Sutra applied here is "All from 9 and the last from 10", and hence we substract 587 from 1000. So the outcome will be (9 -5 = 4, 9 - 8 = 1, 10 - 7 = 3) , and result is 413. Refer to image below for more clarity:

1. Square of Numbers ending in 5.

Step -1 : Multiply the figures (except the last 5) by one more than it.

Step -2 : Write (square of 5)25 after it.

Example -Square -25

(25) ² = [2*(2+1)] 25

=[2*3]25

=625

(105)²= [10*(10*1)]25

=[10*11]25

=11025

Vedic Mathematics is very deep subject.There are unlimited benefits of it.It can help us in many ways.

·         It is very simple, direct, totally unconventional, original and straight forward.
·         It encourages mental calculations.
·         It enriches our understanding of maths and enables us to see links and continuity between different branches of maths.
· Vedic Maths system also gives us a set of checking procedures for independent crosschecking of whatever we do.
· It keeps the mind alert and lively because of the element of choice and flexibility at each .
·   Holistic development of the human brain takes place through Vedic Mathematics along with multidimensional thinking.
· Vedic Mathematics system to quite an extent also helps us in developing our spiritual part of personality.
·   It can introduce creativity in intelligent and smart students, while helping the slow-learners grasp the basic concepts of mathematics. More and more use of Vedic math can without any doubts generate interest in a subject that is generally dreaded by children.

Thus, Vedic maths is considered to be more than the blessing of the Veda for the entire humanity

Here are some important links that can help to understand deeply....

http://www.pebblemaths.org/

http://www.vedicmathschool.com/

http://vedicmathghana.org/

http://hinduism.about.com/od/vedicmaths/a/what_is_vedic_math.htm