VEDIC MATHEMATICS

Introduction

• Author – Bharati Krishna Tirthaji

• Based on Vedas

• Vedic Maths

Ekadhikena PurvenaBy one more than the previous one

Calculate the square of 45.

Multiply the previous digit by one more than itself

452 = 4X5 and 25

= 2025

Calculate the square of:

• 35

1225

•165

27225

Algebraic Proof

• (ax + b)2 = a2x2 + 2abx + b2

• x=10 and b=5

• (10a + 5)2 = 100a2 + 100a + 25

= 100(a)(a+1) + 25

Multiplication of two numbers with sum of unit digits=10 and same rest of the number

Calculate the product of 67 and 63.

Multiply the previous digits by one more than itself and add it to product of unit digits

67 X 63 = 6 X 7 and 7 X 3

= 4221

Calculate:

• 12 X 18

216

• 112 X 118

13216

Algebraic Proof

• (ax + b)(ax + c) = a2x2 + ax(b+c) + bc

• x=10 and b+c=10

• (10a + b)(10a + c) = 100a2 + 100a + bc

= 100(a)(a+1) + bc

Nikhilam navatascaramam DasatahAll from 9 and the last from 10

Calculate the product of 94 and 97.

Base – 10, 100, 1000, etc.

Deviation – Subtract all from 9 and the last from 10

94 - 6

97 - 3

= 9118

Calculate:

• 98 X 97

9506

• 987 X 990

977130

Calculate

• 14 X 12

168

• 998 X 1025

1023000 – 50

1022950

Algebraic Proof

• Base = x, Numbers = a and b

• a=x-d1, b=x-d2

• a X b = (x-d1) X (x-d2)

= x2 – xd1 – xd2 + d1d2

= x(x – d1 –d2) + d1d2

= x(a – d2) + d1d2

Ekanyunena PurvenaOne Less than the previous

Calculate the product of 15 X 999

Useful in multiplication with 9, 99, 999, 9999 and so on

15 X 999 = 15 – 1 =14

999 – 14 =985

= 14985

877 X 9999 = 877 – 1 = 876

9999 – 876 = 9123

= 8769123

Calculate:

• 64 X 99

6336

• 3251 X 9999

32506749

Algebraic Proof

• Numbers = a and b

• a is of form (10x + y) and b is 9, 99, 999….

• (10x + y) X 99 = (10x + y) X (100-1)

= 10(x)(10)2 – 10x + (y)102 – y

= (x)(10)3 + y(10)2 – (10x + y)

= (x)(10)3 + (y-1)(10)2 + (102 – (10x + y))

= (x)(10)3 + (y-1)(10)2 + (99 – (a-1))

Yavadunam Tavadunikrtya Varganca YojayetWhat ever the deficiency subtract that deficit from the number and write along side the square of that deficit

Calculate the square of 96

Useful in obtaining squares of numbers close to bases of powers of 10

962 -> Base = 100

Deficit = 100-96 =4

96-4 =92 and 42 = 16

= 9216

Calculate the squares of:

• 994

988036

• 9988

99760144

Algebraic Proof

• Numbers = a and b

• a is of form (b-d) and b is 10,100,1000,……..

• a2 = (b-d)2 = b2 – 2bd + d2

= b(b – 2d) + d2

= b(b – d – d) + d2

= b(a – d) + d2

Calculate the square of 476

Base = 500 = 5 X 100 Base = 500 = 1000/2

4762 -> Deficit = 24 452/2 = 226

476 – 24 = 452 Ans = (226 X 1000) + 576

452 X 5 = 2260 = 226576

242 = 576

Ans = (2260 X 100) + 576

= 226576

Calculate the square of:

• 395

156025

• 68

4624

BeejankSum of digits of a number

Beejank of 72 = 9,

47 = 1+1 = 2,

68123 = 2+0 = 2

894563912 = 2

Gunita SamuccayahThe whole product is same

67 + 76 = 143

Beejank(67) = 4, 76 =4 and 143 =8

4762 = 226576

Beejank(476) = 8, Beejank(8 X 8) = 1

Beejank(226576) = 1

Just The Beginning• Vast scope of Vedic Maths

• Solves difficult problems with high speed and accuracy

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