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8/22/2019 Vedic Maths-Asin Acoiwpoudtxfnvzi6ybzlesvvdgh3b5v

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VEDICVEDIC

MATHEMATICSMATHEMATICS

-- By Prashanth K NBy Prashanth K N


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What is Vedic Mathematics ?

Vedic mathematics is the namegiven to the ancient system ofmathematics which wasrediscovered from the Vedas.

Its a unique technique ofcalculations based on simpleprinciples and rules , with whichany mathematical problem - be itarithmetic, algebra, geometry ortrigonometry can be solvedmentally.


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Who revived this?Who revived this?

The subject was revived largely due to the efforts ofJagadguru Swami Bharathikrishna Tirthajiof GovardhanPeeth, Puri Jaganath (1884-1960). Having researched the

subject for years, even his efforts would have gone invain but for the enterprise of some disciples who tookdown notes during his last days. That resulted in thebook, Vedic Mathematics, in the 1960s.


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Why Vedic Mathematics?Why Vedic Mathematics? It helps a person to solve problems 10-15 times faster.

It reduces burden (Need to learn tables up to nine only)

It provides one line answer.

It is a magical tool to reduce scratch work and finger counting. It increases concentration.

Time saved can be used to answer more questions.

Improves concentration.

Logical thinking process gets enhanced.


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Base of Vedic MathematicsBase of Vedic Mathematics

Vedic Mathematics

now refers to a set of

sixteen mathematical

formulae or sutras and

their corollaries

derived from the Vedas.


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Base of Vedic MathematicsBase of Vedic Mathematics

Vedic Mathematicsnow refers to a set

of sixteenmathematicalformulae or sutrasand theircorollaries derived

from the Vedas.


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EKDHIKENA PRVEAEKDHIKENA PRVEA

The Sutra

(formula)

Ekdhikena

Prvena means:

By one more than

the previous one.

This Sutra is

used to the

Squaring ofnumbers ending

in 5.


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Squaring of numbers ending in

5.

Conventional Method

65 X 65

6 5

X 6 5

3 2 53 9 0 X

4 2 2 5

Vedic Method

65 X 65 = 4225

( 'multiply the

previous digit 6 byone more thanitself 7. Than write25 )


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Corollary to Ekadhikena purvenaCorollary to Ekadhikena purvena

Squaring a number that does not end in 5.

This method requires rounding a number up and down based on thenearest base of 10 or 100, multiplying the two numbers, then addingthe square of the number added and subtracted. I'll explain with two examples:

Rounding to base-100: To find the square of 96, you would round up to 100.Since you added 4, you now subtract 4 from 96 to yield 92. Multiply 92 and100. This can be easily done in one's head: 9200. Since you added andsubtracted 4, square the 4 to yield 16. Now add 16 to 9200. Thus, 96 squared is9216.

Rounding to base-10: To find the square of 57, you would round up to 60. Sinceyou added 3, you now subtract 3 from 57 to yield 54. Multiply 60 by 54 (somepeople can do this in their head). The answer is 3240. Since you added andsubtracted 3, square it. That makes 9. Add 9 to 3240. The square of 57 is 3249.


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NIKHILAM AVATASCHARAMAMNIKHILAM AVATASCHARAMAM

DASATAHDASATAHThe Sutra (formula)

NIKHILAM

NAVATASCHARAMAM DASATAH

means :

all from 9 and thelast from 10

This formula canbe very effectively

applied inmultiplication ofnumbers, which arenearer to bases like

10, 100, 1000 i.e., tothe powers of 10(eg: 96 x 98 or 102x 104).


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Case I :When both the numbers are lower

than the base.

Conventional Method

97 X 94

9 7

X 9 4

3 8 8

8 7 3 X

9 1 1 8

Vedic Method

9797 33

XX 9494 669 1 1 89 1 1 8


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Case ( ii) : When both theCase ( ii) : When both the

numbers are higher than the basenumbers are higher than the base Conventional

Method

103 X 105

103

X 105

5 1 5

0 0 0 X1 0 3 X X

1 0, 8 1 5

Vedic Method

For Example103 X 105For Example103 X 105

103103 33

XX 105 55

1 0, 8 1 5


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Case III: When one number is moreCase III: When one number is more

and the other is less than the base.and the other is less than the base.

Conventional Method

103 X 98103

X 98

8 2 4

9 2 7 X

1 0, 0 9 4

Vedic Method

103103 33

XX 98 -2

1 0, 0 9 4


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NURPYENA

The Sutra (formula)

NURPYENA

means :

'proportionality'

or'similarly'

This Sutra is highlyThis Sutra is highlyuseful to finduseful to find

products of twoproducts of twonumbers whennumbers whenboth of them areboth of them arenear the Commonnear the Common

bases like 50, 60,bases like 50, 60,200 etc (multiples200 etc (multiplesof powers of 10).of powers of 10).


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NURPYENA

Conventional Method

58 X 485 8

X 4 8

4 6 42 4 2 X

2 8 8 4

Vedic Method

5858 88XX 4848 --22

2 82 8 8 4


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NURPYENA

Conventional Method

46 X 43

4 6

X 4 3

1 3 81 8 4 X

1 9 7 8

Vedic Method

4646 --44

XX 43 --77

1 9 7 8


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URDHVATIRYAGBHYAM

The Sutra (formula)

URDHVA

TIRYAGBHYAMmeans :

Vertically and cross

wise

This the generalThis the generalformula applicableformula applicable

to all cases ofto all cases ofmultiplication andmultiplication andalso in the divisionalso in the divisionof a large numberof a large number

by another largeby another largenumber.number.


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Two digit multiplication byby

URDHVA TIRYAGBHYAMThe Sutra (formula)

URDHVA

TIRYAGBHYAMmeans :

Vertically and cross

wise

Step 1Step 1: 5: 52=10, write2=10, writedown 0 and carry 1down 0 and carry 1

Step 2Step 2: 7: 72 + 52 + 53 =3 =

14+15=29, add to it14+15=29, add to itprevious carry over valueprevious carry over value1, so we have 30, now1, so we have 30, nowwrite down 0 and carry 3write down 0 and carry 3

Step 3Step 3: 7: 73=21, add3=21, add

previous carry over valueprevious carry over valueof 3 to get 24, write itof 3 to get 24, write itdown.down.

So we have 2400 as theSo we have 2400 as theanswer.answer.


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Two digit multiplication byby

URDHVA TIRYAGBHYAMVedic Method

4 6

X 4 3

1 9 7 8


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Three digit multiplication by

URDHVATIRYAGBHYAMVedic Method

103

X 105

1 0, 8 1 5


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YAVDUNAM TAAVDUNIKRITYA

VARGANCHAYOJAYETThis sutra means

whatever the extent

of its deficiency,lessen it stillfurther to that veryextent; and also set

up the square ofthat deficiency.

This sutra is veryhandy in

calculating squaresof numbersnear(lesser) topowers of 10


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YAVDUNAM TAAVDUNIKRITYAVARGANCHAYOJAYET

982

= 9604

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

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

Decrease the given number further by anDecrease the given number further by anamount equal to the deficiency. i.e.,amount equal to the deficiency. i.e.,perform ( 98perform ( 98 --2 ) = 96. This is the left side2 ) = 96. This is the left sideof our answer!!.of our answer!!.

On the right hand side put the square ofOn the right hand side put the square of

the deficiency, that is square of 2 = 04.the deficiency, that is square of 2 = 04.

Append the results from step 4 and 5 toAppend the results from step 4 and 5 toget the result. Hence the answer is 9604.get the result. Hence the answer is 9604.

NoteNote :: While calculating step 5, the number of digits in the squared number (04)While calculating step 5, the number of digits in the squared number (04)

should be equal to number of zeroes in the base(100).should be equal to number of zeroes in the base(100).


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YAVDUNAM TAAVDUNIKRITYAVARGANCHAYOJAYET

1032= 10609

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

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

Increase the given number further by anIncrease the given number further by anamount equal to the surplus. i.e., perform (amount equal to the surplus. i.e., perform (103 + 3 ) = 106. This is the left side of our103 + 3 ) = 106. This is the left side of ouranswer!!.answer!!.

On the right hand side put the square ofOn the right hand side put the square of

the surplus, that is square of 3 = 09.the surplus, that is square of 3 = 09.

Append the results from step 4 and 5 toAppend the results from step 4 and 5 toget the result.Hence the answer is 10609.get the result.Hence the answer is 10609.

NoteNote :: while calculating step 5, the number of digits in the squared number (09)while calculating step 5, the number of digits in the squared number (09)

should be equal to number of zeroes in the base(100).should be equal to number of zeroes in the base(100).


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YAVDUNAM TAAVDUNIKRITYA

VARGANCHAYOJAYET

10092

= 1018081


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Multiplying numbers by 11

To multiply any 2-figure number by 11 we just

put the total of the two figures between

the 2 figures.

26 X 11 = 286

72 X 11 = 792

77 X 11 = 847


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Multiplying numbers by 12

To multiply any 2-figure number by 12 we

double the last digit, put the total of the

twice the first digit and the 2nd

digit.

13 X 12 = 156

14 X 12 = 168


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SAKALANA

VYAVAKALANBHYAMThe Sutra (formula)

SAKALANA

VYAVAKALANBHYAMmeans :

'by addition and by

subtraction'

It can be applied inIt can be applied insolving a special typesolving a special typeof simultaneousof simultaneous

equations where theequations where thexx -- coefficients andcoefficients andthe ythe y -- coefficientscoefficientsare foundare found

interchanged.interchanged.


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SAKALANA

VYAVAKALANBHYAMExample 1:

45x 23y = 113

23x 45y = 91

Firstly add them,Firstly add them,

( 45x( 45x 23y ) + ( 23x23y ) + ( 23x 45y ) = 113 + 9145y ) = 113 + 91

68x68x 68y = 20468y = 204

xx y = 3y = 3

Subtract one from other,Subtract one from other,

( 45x( 45x 23y )23y ) ( 23x( 23x 45y ) = 11345y ) = 113 9191

22x + 22y = 2222x + 22y = 22

x + y = 1x + y = 1

Rrepeat the same sutra,Rrepeat the same sutra,

we getwe getx = 2x = 2 andand y =y = -- 11


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SAKALANA

VYAVAKALANBHYAMExample 2:

1955x 476y =2482

476x 1955y = - 4913

Just add,Just add,

2431( x2431( x y ) =y ) = -- 24312431

xx y =y = --11 Subtract,Subtract,

1479 ( x + y ) = 73951479 ( x + y ) = 7395

x + y = 5x + y = 5

Once again add,Once again add,2x = 42x = 4 x = 2x = 2

subtractsubtract

-- 2y =2y = -- 66 y = 3y = 3


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ANTYAYORDAAKE'PI

The Sutra (formula)

ANTYAYOR

DAAKE'PI

means :

Numbers of which

the last digits addedup give 10.

This sutra is helpful inThis sutra is helpful inmultiplying numbers whose lastmultiplying numbers whose lastdigits add up to 10(or powers ofdigits add up to 10(or powers of10). The remaining digits of the10). The remaining digits of the

numbers should be identical.numbers should be identical.

For ExampleFor Example: In multiplication: In multiplicationof numbersof numbers

25 and 25,25 and 25,

2 is common and 5 + 5 = 102 is common and 5 + 5 = 10

47 and 43,47 and 43,

4 is common and 7 + 3 = 104 is common and 7 + 3 = 10

62 and 68,62 and 68,

116 and 114.116 and 114.

425 and 475425 and 475


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ANTYAYORDAAKE'PI

Vedic Method

6 7

X 6 3

4 2 2 1

The same rule works whenThe same rule works whenthe sum of the last 2, lastthe sum of the last 2, last3, last 43, last 4 -- -- -- digits addeddigits added

respectively equal to 100,respectively equal to 100,1000, 100001000, 10000 ---- -- -- ..

The simple point toThe simple point toremember is to multiplyremember is to multiplyeach product by 10, 100,each product by 10, 100,1000,1000, -- -- as the case mayas the case may

be .be .

You can observe that this isYou can observe that this ismore convenient whilemore convenient whileworking with the productworking with the productof 3 digit numbersof 3 digit numbers


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ANTYAYORDAAKE'PI

892 X 808

= 720736

Try Yourself :Try Yourself :

A)A) 398 X 302398 X 302= 120196= 120196

B)B) 795 X 705795 X 705

= 560475= 560475


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LOPANASTHPANBHYM

The Sutra (formula)

LOPANASTHPANBHYM

means :

'by alternate

elimination and

retention'

Consider the case ofConsider the case offactorization of quadraticfactorization of quadraticequation of typeequation of type

axax22 + by+ by22 + cz+ cz22 + dxy + eyz + fzx+ dxy + eyz + fzx

This is a homogeneousThis is a homogeneousequation of second degreeequation of second degree

in three variables x, y, z.in three variables x, y, z.

The subThe sub--sutra removes thesutra removes thedifficulty and makes thedifficulty and makes thefactorization simple.factorization simple.


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LOPANASTHPANBHYM

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;factorize3x 2 + 11xz + 6z 2 = (3x + 2z) (x + 3z)

Fill the gaps, the given expression

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

Eliminate z by putting z = 0Eliminate z by putting z = 0and retain x and y andand retain x and y andfactorize thus obtained afactorize thus obtained aquadratic in x and y by meansquadratic in x and y by means

ofof AdyamadyenaAdyamadyena sutra.sutra.

Similarly eliminate y andSimilarly eliminate y andretain x and z and factorizeretain x and z and factorizethe quadratic in x and z.the quadratic in x and z.

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

factors of the expression.factors of the expression.


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GUNTASAMUCCAYAH -

SAMUCCAYAGUNTAHExample :

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;factorize3x 2 + 11xz + 6z 2 = (3x + 2z) (x + 3z)

Fill the gaps, the given expression

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

Eliminate z by putting z = 0Eliminate z by putting z = 0and retain x and y andand retain x and y andfactorize thus obtained afactorize thus obtained aquadratic in x and y by meansquadratic in x and y by means

ofof AdyamadyenaAdyamadyena sutra.sutra.

Similarly eliminate y andSimilarly eliminate y andretain x and z and factorizeretain x and z and factorizethe quadratic in x and z.the quadratic in x and z.

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

factors of the expression.factors of the expression.


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ReferencesReferences

y "VEDICMATHEMATICS"by H.H. Jagadguru SwamiSri Bharati Krishna TirthajiMaharaj.

Publishers Motilal Banarasidass, BunglowRoad, JawaharNagar,Delhi 110 007; or

Chowk, Varanasi (UP); or Ashok Raj Path, Patna, (Bihar)

y

www.vedicmaths.org


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Vedic Mathematics

And, you thought biggest

contribution of Indians to field of

Mathematics was Zero??

- Thank You !

vedic maths-asin acoiwpoudtxfnvzi6ybzlesvvdgh3b5v

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