Vedic Mathematics-Final

8/7/2019 Vedic Mathematics-Final

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Vedic Mathematics

By

Dr. SUDHA GUPTA

Department of Mathematics

Lakshmibai College, University ofDelhi


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What is Vedic Mathematics ?

It is an ancienttechnique, which

simplifies multiplication, divisibility,

complex numbers, squaring, cubing,

square and cube roots. Even recurring

decimals and auxiliary fractions can

be handled by Vedic Mathematics.


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Who Brought Vedic Mathematics

to Limelight ?

Theancientsystems of Mathematics

wasrediscovered from VedasbyJagadguru Swami

Bharathikrishna Tirthaji of

Govardhan Peeth, Puri Jaganath

(1884-1960)


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What is the basis of Vedic

Mathematics ?

16 Sutras&

13 Sub-Sutras


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Vedic Mathematical Sutras

,dkf/kdsu iwosZ.k

Ekadhikena Purvena

(vkuq:I;s)kwU;eU;r~

(Anurupye) Sunyamanyat

O;f"Vlef"V%

Vyastisamastih

fuf[kya uorpjea nkr%

Nikhilam

NavatascaramamDasatah

LkadyuO;odyukH;ke~

Sankalana

vyavakalanabhyam

ks"kk.;~dsu pjes.k

Sesanyankena

Caramena

/oZfr;ZXHk;ke~

Urdhva-tiryagbhyam

Ikwj.kkiwj.kkH;ke~

Puranapuranabhyam

LkksikUR;};eUR;e~

Sopantyadvayamantyam

IkjkoR;Z ;kst;sr~Paravartya Yojayet

PkyudyukH;ke~Calana-Kalanabhyam

,dU;wusu iwosZ.kEkanyunena Purvena

kwU;a lkE;leqPp;s

Sunyam Samyasamuccaye

;konwue~

Yavadunam

Xkqf.krleqPp;%

Gunitasamuccayah

Xkq.kdleqPp;%

Gunakasamuccayah


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Multiplication of Numbers

Thesutra whichis used for

multiplicationis:fuf[kya uorpjea nkr%

W

hich literally translated,means ;All from9andthe last from10


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Procedure for Multiplication

Suppose we have to multiply 9 by 7

We should take, as base for our calculations,that power of 10 which is nearest to thenumbers to be multiplied. In this case 10itselfis that power;

Put t h e two numbers 9 and 7 above andbelow on the left hand side.

Subtract each ofthem from the base (10) andwrite down the remainders (1 and 3) on theright hand side with a connecting minus sign( - ) between them to show that the numbers

to be multiplied are both ofthem less that 10. The product will have two parts one on the

left side and one on the right. A verticaldividing line may be drawn for the purpose ofdemarcation ofthe two parts.

Now, the left hand side digit (ofthe answer)can be arrived at in one of4 ways:-

Subtractthebase10 fromthesum ofthegivennumbers(9and 7 i.e.16)andput(16-10)i.e.6asthe lefthandpart oftheanswer.

9 + 7 10 = 6

orSubtractthesum ofthetwodeficiencies(1+3=4) fromthebase(10)

10 1 3 = 6

orCross subtractdeficiency (3) onthesecondrow fromthe original number(9)inthe firstrow.

9 3 = 6 orCross subtractintheconverse way

(i.e.1 from 7).

7 1 = 6

Now, Vertically mulitply thetwo deficitfigures(1and3).Theproductis3.Andthis

istherighthandsideportion oftheanswer. Thus9 x 7 = 63


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Multiplication of Numbers

Next Sutrais

/oZfr;ZXHk;ke~(Urdhvatriyagbhayam)

whichmeansVertically and Crosswise


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12 X 13

Suppose we have to multiply 12 by 13

We multiply the left hand most digits 1 of the

multiplicand vertically by the left hand most digits1 of the multiplier, get their product 1 and set itdown as the left hand most part ofthe answer.

We then multiply 1 and 3 ; 1 and 2 crosswise, addthe two, get 5 as the sum and set it down as themiddle part ofthe answer.

We multiply 2 and 3 vertically, get 6 as theirproduct and put it down as the last (the right handmost) part ofthe answer.

Thus 12 x 13 = 156


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Special Sub-Sutra for Multiplication by 11

vUR;;ksjso (Antyayoreva)

which means Only the last two digits

The following example illustrate this very easy methods.13 423 x 11

Write down the numberwith naught placed at both ends. This is a

naught sandwich 0 1 3 4 2 3 0

Add the final two digits, 3 + 0 = 3 and write the answer below 0 .0 1 3 4 2 3 0

3

For the tens digit, add the final two digits to that point, that is 2 + 3 = 5.

0 1 3 4 2 3 0

5 3 Continue to add adjacent digits, that is 4+2 = 6, 3+4=7, 1+3 = 4,

and 0+1=1

0 1 3 4 2 3 0

1 4 7 6 5 3

The answer is 1 4 7, 6 5 3 2


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Multiplication by 12

The sutra used to obtained the product of any

number with 12 is

LkksikUR;};eUR;e~(Sopantyadvayamantyam)

which means

The ultimate and twice the penultimate

This is very similar to multiplication by 11

but we just double the digitto the left

before adding


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Multiplication by 12

For example : 6 5 2 1 4 x 12

we start with the noughtsandwich 0 6 5 2 1 4 0

The ultimate digit is 0 andthe penultimate digits is 4, so

the ultimate plus twice thepenultimate is 0 + 8 = 8.

0 6 5 2 1 4 0

8

For the tens column, theultimate is 4 and thepenultimate is 1, so 4+2= 6.

0 6 5 2 1 4 0

6 8

Likewise, 1 + 4 = 5, and 2 +10 = 12. With 12 we setdown 2 and carry 1.

0 6 5 2 1 4 0

2 5 6 8

1

5 + 12 + Carry 1 = 18 andagain we carry 1.

The final step is 6 + 0 + Carry1 = 7.

0 6 5 2 1 4 0

7 8 2 5 6 8

1 1

The answer is 7

82 5 6

8


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Thankyou

Vedic Mathematics-Final

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