Vedic Mathematics Worlds Fastest Mental Math System

8/12/2019 Vedic Mathematics Worlds Fastest Mental Math System

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By Abhishek Sharma



What is Vedic Mathematics ?

Vedic mathematics is the namegiven to the ancient system ofmathematics in India.

It‟s a unique technique ofcalculations based on simpleprinciples and rules , with which anymathematical problem - be itarithmetic, algebra, geometry ortrigonometry can be solved

mentally.



Why Vedic Mathematics?

It helps to solve problems much faster.

It reduces burden of long mental calculations.

It provides one line answer.

It is a magical tool to reduce scratch work and counting onfingers.

It increases concentration. Time saved can be used to answer more questions.

Logical thinking process gets enhanced.



Base of Vedic Mathematics

Vedic Mathematicsnow refers to a setof sixteen

mathematicalformulae or sutrasand their corollariesderived from the

Vedas.

Text on left is in Sanskrit LanguageExplanation given on right.



Base of Vedic Mathematics

Vedic Mathematicsnow refers to a setof sixteen

mathematicalformulae or sutrasand their corollariesderived from the

Vedas.





Example: „Squaring of numbers ending in 5‟.

Conventional Method

65 X 656 5

X 6 5

3 2 5

3 9 0 X4 2 2 5

Vedic Method

65 X 65 = 4225

( 'multiply the previousdigit 6 by one morethan itself 7. Thanwrite 25 )



NIKHILAM NAVA TAS‟ CHARA MAM DASA TAH“all from 9 and the last from 10”

The Sutra (formula)NIKHILAMNAVATAS‟CHARAMA

M DASATAH means :

“all from 9 and the lastfrom 10”

This formula can bevery effectivelyapplied in

multiplication ofnumbers, which arenearer to bases like10, 100, 1000 i.e.,

to the powers of 10(e.g.: 96 x 98 or 102x 104).



Case I :When both the numbers are lower than the base.

Conventional Method

97 X 94

9 7

X 9 4

3 8 88 7 3 X

9 1 1 8

Vedic MethodBase is 100

97 3 (100- 97)X 94 6 (100 – 94)

9 1 1 894-3 3x6

94 6X 97 3

9 1 1 897-6 6x3

Subtract difference of upper number fromlower number and multiply both differences.



Case ( ii) : When both the numbers are higher thanthe base

Conventional Method103 X 105

103

X 1055 1 5

0 0 0 X1 0 3 X X

1 0, 8 1 5

Vedic Method

For Example103 X 105

103 3 (100+3)X 105 5 (100+5)

1 0, 8 1 5105+3 3x5

Add lower number 105 and with uppernumber‟s difference 3 that‟s the left partand multiply both differences 3 and 5that‟s the right part



Case III: When one number is more and the other isless than the base.

Conventional Method

103 X 98

103

X 98

8 2 4

9 2 7 X

1 0, 0 9 4

Vedic Method

103 3 (100+3)X 98 -2 (100-2)

98+3 / 3x2101 / 06( 101-1)/(100-06)Ans: 1 00 9 4

Steps:1. Add lower number and upper‟sdifference subtract one fromresult that‟s left part

2. Multiply both differences andsubtract it from 100 this is rightpart



ĀNURŨPYENA' proportionality „ or 'similarly '

The Sutra (formula)ĀNURŨPYENA means :

' proportionality 'or

'similarly '

This Sutra is highlyuseful to findproducts of two

numbers when both ofthem are near theCommon bases like50, 60, 200 etc

(multiples of powersof 10).



ĀNURŨPYENA' proportionality „ or 'similarly '

Conventional Method

46 X 434 6

X 4 3

1 3 8

1 8 4 X1 9 7 8

Vedic Method

Working base 100/2= 50

46 -4 (50-4)X 43 -7 (50-7)(43-4) (4x7)39 / 2819 ½ / 28 ( 39 divide by 2 )

19/ (50 + 28)( Half of 100 to be added to 28) since we have ½had it been divisible by 2 we would have left it

as is.)

19 /78Ans: 1 9 7 8





URDHVA TIRYAGBHYAM“Vertically and cross wise”

The Sutra (formula)

URDHVATIRYAGBHYAMmeans :

“Vertically and crosswise”

This the general

formula applicable

to all cases of

multiplication and

also in the division

of a large number

by another largenumber.



Two digit multiplication by URDHVA TIRYAGBHYAM

The Sutra (formula)

URDHVATIRYAGBHYAMmeans :

“Vertically and crosswise”

E.g. 75X 322400

Step 1: 5×2=10, write down

0 and carry 1 Step 2: 7×2 + 5×3 =

14+15=29, add to it previouscarry over value 1, so wehave 30, now write down 0

and carry 3 Step 3: 7×3=21, add

previous carry over value of3 to get 24, write it down.

So we have 2400 as the

answer.



Two digit multiplication by URDHVA TIRYAGBHYAM

Vedic Method4 6

X 4 3

1 9 7 8

Step1: 6x3=18 write 8 carry 1

Step2:

4x6+4x3=24+12=36+carry =37

write 7 carry 3

Step3: 4x4 = 16 + carry 3 = 19

write 19

Ans : 19/7/8 or 1978



Three digit multiplication byURDHVA TIRYAGBHYAM

Vedic Method

103

X 105

1 0, 8 1 5

Step1: 3x5=15 carry 1 write 5

Step2: 0x3=0x5 = 0 + carry 1

Write 1

Step3: 1x5+0x0+3x1=5+0+3=8

Write 8

Step4: 1x0+1x0=0 write 0

Step5: 1x1=1 write 1

Ans : 10815



YAVDUNAM TAAVDUNIKRITYA VARGANCHA YOJAYET“Squares of numbers near(lesser) to powers of 10“

This formulae meanswhatever the extentof its deficiency,

lessen it still furtherto that very extent;and also set up thesquare of thatdeficiency.

This formulae is veryhandy in calculatingsquares of numbers

near(lesser) to powersof 10



YAVDUNAM TAAVDUNIKRITYA VARGANCHA YOJAYETSquares of numbers near(lesser) to powers of 10

982

= 9604

Base 100100-2 = 98

(98-2)/2x2

96/04

Ans: 9604

The nearest power of 10 to 98 is 100. Therefore,let us take 100 as our base.

Since 98 is 2 less than 100, we call 2 as thedeficiency.

Decrease the given number further by anamount equal to the deficiency. i.e., perform ( 98-2 ) = 96. This is the left side of our answer!!.

On the right hand side put the square of thedeficiency, that is square of 2 = 04.

Append the results from step 4 and 5 to get theresult. Hence the answer is 9604.

Importan t : Whi le calculat ing step 5, the num ber of d ig i ts in the s quared

number (04) shou ld be equal to number of zeroes in the base(100).




1032

= 10609

Base 100

(100+3)

103+3= 106

3x3= 09

10609

Ans: 10609

The nearest power of 10 to 103 is 100.Therefore, let us take 100 as our base.

Since 103 is 3 more than 100 (base), we call 3as the surplus.

Increase the given number further by anamount equal to the surplus. i.e., perform ( 103+ 3 ) = 106. This is the left side of our answer!!.

On the right hand side put the square of thesurplus, that is square of 3 = 09.

Append the results from step 4 and 5 to getthe result. Hence the answer is 10609.

Important: while calculating step 5, the number of digits in the squarednumber (09) should be equal to number of zeroes in the base(100).




Another example:

10092= 1018081

Base 1000

1000+9

1009+9=1018

9x9=081 (since base has three zeros)

1018/081Ans: 1018081



SAŃKALANA – VYAVAKALANĀBHYAM'by addition and by subtraction'

The Sutra (formula)

SAŃKALANA –VYAVAKALANĀBHYA

Mmeans :

'by addition and by

subtraction'

It can be applied in solving

a special type of

Simultaneous equations

Where the x - coefficients

and the y - coefficients

are found interchanged.





SAŃKALANA – VYAVAKALANĀBHYAM'by addition and by subtraction'

Example 2:

1955x – 476y =

2482476x – 1955y = -

4913

Just add,

2431( x – y ) = - 2431

x – y = -1

Subtract,

1479 ( x + y ) = 7395

x + y = 5

Once again add,

2x = 4 x = 2subtract

- 2y = - 6 y = 3



ANTYAYOR DAŚAKE'PI„ Numbers of which the last digits added up give 10.‟

The Sutra (formula)

ANTYAYORDAŚAKE'PImeans :

„ Numbers of which thelast digits added up

give 10.‟

This sutra is helpful inmultiplying numbers whose lastdigits add up to 10(or powers of10). The remaining digits of the

numbers should be identical.For Example: In multiplication of

numbers 25 and 25,

2 is common and 5 + 5 = 10 47 and 43,4 is common and 7 + 3 = 10

62 and 68, 116 and 114.

425 and 475




Vedic Method6 7X 6 3

4 2 2 1

The same rule works whenthe sum of the last 2, last 3,last 4 - - - digits addedrespectively equal to 100,

1000, 10000 -- - - . The simple point to

remember is to multiply eachproduct by 10, 100, 1000, - -as the case may be .

You can observe that this ismore convenient whileworking with the product of 3digit numbers




892 X 808= 720736

Try Yourself :

A) 398 X 302

= 120196

B) 795 X 705

= 560475



LOPANA STHÂPANÂBHYÂM'by alternate elimination and retention'

The Sutra (formula)

LOPANASTHÂPANÂBHYÂMmeans :

'by alternateelimination andretention'

Consider the case offactorization of quadraticequation of type

ax2 + by2 + cz2 + dxy + eyz + fzx

This is a homogeneous equationof second degree in threevariables x, y, z.

The sub-sutra removes thedifficulty and makes thefactorization simple.



LOPANA STHÂPANÂBHYÂM'by alternate elimination and retention'

Example :

3x 2 + 7xy + 2y 2+ 11xz + 7yz + 6z 2

Eliminate z and retain x, y ;

factorize3x 2 + 7xy + 2y 2 = (3x + y) (x +2y)

Eliminate y and retain x, z;factorize

3x 2 + 11xz + 6z 2 = (3x + 2z) (x+ 3z)

Fill the gaps, the givenexpression

(3x + y + 2z) (x + 2y + 3z)

Eliminate z by putting z = 0 andretain x and y and factorize thusobtained a quadratic in x and yby means of Adyamadyena

sutra.

Similarly eliminate y and retain xand z and factorize thequadratic in x and z.

With these two sets of factors,fill in the gaps caused by theelimination process of z and yrespectively. This gives actual

factors of the expression.



Thank you

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Vedic Mathematics Worlds Fastest Mental Math System

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