Back of The Book
What is Vedic Mathematics?
Vedic Mathematics is ancient system of mathematics which was formulated and encapsulated in modern from by jagadguru Swami Bharthi Krishna Tirtha ji. He is the 143rd Shankaracharya of Goverdhan Peeth, Pur. He formulated sixteen sutras and thirteen upasutras. These sutras can be applied effectively in conventional mathematics for faster solutions than the methods usually being.
Why should one know Vedic mathematics?
The solution of the problem can be viewed in different dimensions, providing variety of ways to get the answer which is derived in a simple, fast and accurate manner.
How effective are Vedic math techniques?
Multiplication tables up to 5 are sufficient to solve a problem in Vedic Maths. It has the capability of performing multiple operations at one timeVedic mathematics optimally utilizes both hemispheres of the brain is the seat of language and processes in a logical and sequential order, while the right side is visual(spatial), intuitive, random booting of memory and concentration.
Will it support school curriculum?
The Vedic Maths methods are parallel and supplemental to the school study. It does not confuse the child. Vedic Maths focus is on mastering the core skills that a child needs: to be successful in secondary education and beyond.The course syllabus can be designed dynamically in tandem with the school curriculum. This helps developing the mental abilities of a child. We can custom design Vedic Maths course according to the school academic requirements.
Will Vedic Maths be useful for higher classes?
Yes, concepts such as Quadratic Equations Simulatneous Equations, Trigonometry and even Calculus have been mad simple and easier Vedic mathematics.
Will Vedic Maths help a student to minimize careless mistakes?
In Vedic mathematics the oneline mental formulae have an inbuilt series o verifying methods. Therefore the chance for a wrong answer is minimized.
Shriram M. Chauthaiwale M.Sc. B.Ed working as lecturer in Mathematics since 30 years. He published 3 books on history of mathematics and 1 on Vedic mathematics with CD. 20 odd research papers published in national and international journals and conferences. Numerous articles in news papers and magazines. All india radio talk and Doodarshan T.V. program on Vedic Mathematics since 2008.
Dr. Ramesh completed M.Sc. and Ph.D in Statistics from Indian Agricultural Research Institute, New Delhi. Worked as a Technical consultant for software development for one year, but his fascination for numbers found a creative channel when he joined as the Head of Vedic Mathematics Department, Ved Vignan Maha Vidya Peeth (VVMVP) The Art of Living Foundation in July 2006.
Trained more than 120 teachers in Vedic Mathematics. Taken Vedic Mathematics (classroom and online) courses for national and international participants. Had given talk on Vedic Mathematics in World Space Radio.
In India higher and evolved forms of mathematics were in practice since the Vedic times as well seen through the instances found in the Vedas and related literature.
Swami Bharthi Krisna Tirtha (143rd Shankaracharya of Govardhana Peeth, Puri) derived 16 Sutras and 13 Upasutras which can be universally applied in various disciplines of mathematics. He followed the same tradition while explaining mathematics principles and procedueres.
These Sutras were found to be very effective and enjoyable, with the help of which many mathematics operations ranging from simple additionsubtraction to more difficult topics like Algebra, Differentiation, Integration, Trigonometry an Gemotry can be solved with ease. He gave his methods the name Vedic Mathematics through many misunderstand Vedic Mathematics to being the mathematical concepts enumerated in the Vedas.
The Beauty of Vedic Mathematics is it approaches through simple and direct, single line, nonmonotonic, multichoice, direction independent and faster methods unlike conventional mathematics. This definitely leaves behind wide options in the methodologies to be chosen. Vedic maths ensures a balanced utility of both the right and left brain (logic and creativity respectively). Through Vedic Mathematics the path to infinite wisdom on maths is enjoyable and creative.
Contents

9  
1.1  Numbers and Arithmetic  11  
1.2  Algebra  12  
1.3  Geometry  13  
Intorduction to Vedic Mathematics  17  
2.1  Life and works of Bharati Krishna Teertha Ji  17  
2.2  Art of Living' and Vedic Mathematics  21  
2.3  Advantages of Vedic Mathematics  22  
Sutras  24  
3.1  Meaning of the Sutras  24  
3.2  Sapta Sutrani (Seven Sutras)  27  
3.3  Pancha Upsutrani (Five Upasutra)  29  
3.4  Other UpSutras  31  
Fundamental Concepts  33  
Definations  33  
4.1  Complement of the number (Purakanka)  34  
4.2  Digital Root of the Number  36  
4.3  Vinculum Numbers  37  
4.4  Normal toVinculum Conversion  38  
4.5  Vinculum to Normal Conversion  40  
4.6  Multiplication Tables  40  
Operators  42  
Additon  48  
5.1  Placewise Addition Method  48  
5.2  Addition by Shuddha Method  50  
Subtraction of the Numbers  53  
6.1  Subtraction by Shuddha Method  53  
6.2  Vinculum Subtraction  56  
6.3  Simultaneous Addition and Substraction  58  
Urdhvatiryak Multiplication  60  
7.1  Single Digit Multiplier  61  
7.1.1  1 x 1 Multiplication  61  
7.1.2  2 x 1 Multiplication  61  
7.1.3  3 x 1 Multiplication  63  
7.1.4  4 x 1 Multiplication  64  
7.2  TwoDigit Multiplier  66  
7.2.1  2 x 2 Multiplication  66  
7.2.2  3 x 2 Multiplication  68  
7.2.3  4 x 2 Multiplication  70  
7.3  ThreeDigit Multiplier  71  
7.3.1  3 x 3 Multiplication  71  
7.3.2  4 x 3 Multiplication  73  
7.4  FourDigit Multiplier  75  
7.4.1  4 x 4 Multiplication  75  
7.5  Decimal Number Multiplications  77  
Multiplications  80  
(Some Special Cases)  80  
8.1  Antyayordashke'pi_10 Multiplication  81  
8.2  Antyayordashke'pi_100 Multiplication  84  
8.3  Antyayordashke'pi_1000 Multiplication  86  
8.4  Multiplier is 9,99,999 or 9999  88  
8.4.1  Equal number of digits in multiplicand and Multiplier  88  
8.4.2  Lesser number of digits ni multiplicand  91  
Alogorithim  91  
8.4.3  Multiplicand with grater number of digits  92  
8.5  Multiplication by 11  94  
8.6  Multiplication by 101  96  
8.7  Multiplication by 1001  98  
Sum of Products & Product of Sums  101  
9.1  The Sum of Products: Single digit multiplier  101  
9.2  Sum of Products: Two digit multiplier  104  
9.3  Sum of Products: Three and Four digit multiplier  107  
9.4  Sum of Products of Decimal number  109  
9.5  The Product of Sums and differences  111  
Base Multiplication  116  
10.1  Definitions  
10.2  (a) Near to base 10  118  
10.2  (b) Near to working base m x 10  120  
10.3  (a) Near to base 100  122  
10.3  (b) Near to working base m x 100  123  
10.4  (a) Near to base 1000  124  
10.4  (b) Near to working base m x 1000  126  
10.05  Very near numbers (Nikhilam Method)  127  
Squares  131  
11.1  Anurupyena Method  131  
11.2  Duplex Method  133  
11.2  (a) Square of twodigit number  134  
11.2  (b) Square of threedigit number  136  
11.2  (c) Square of fourdigit number  138  
11.3  Square of the number by Nikhilam method  139  
11.4  Square of Number ending with 5  142  
11.5  Squares of numbers near 50, 500 or 5000  143  
Sum/Products of Squares  146  
12.1  Duplex Method for Sum and Difference of Squares  146  
12.2  Nikhilam Method for Sum and difference of Squares  149  
12.3  Multiplication with squares of a Number  152  
Cubes  156  
13.1  Anurupyena Method for Cube of number  156  
13.2  Sum or Difference of Cubes  159  
13.3  Nikhilam Method for Cube of Number  160  
13.4  Product with Cubes of Two digit Numbe  164  
Dhajanka Division  167  
14.1  Division with Single Digit Divisor  167  
14.2  Division with Two Digit Divisor  170  
14.3  Division with Three Digit Divisor  174  
14.4  Division with Four Digit Divisor  177  
Division of Sums/Products  180  
15.1  Division of Sums  181  
15.2  Division of Product  185  
15.3  Division of Sums of Products  189  
15.4  Division of Product of Sums  192  
15.5  Division of Squares and Cubes  194  
Square Roots of Number  197  
16.1  Facts of Note  197  
16.2  Square Roots by Vilokanam  199  
16.3  Square Roots by Dwandvayoga Method  201  
16.4  Square Roots of Sum or Product of Numbers  250  
16.5  Square Roots of Sums of Squares  208  
Cube Roots  211  
17.1  Facts of Note  211  
17.2  Cube Roots by Vilokanam  213  
17.3  Cube Roots by Division Method  215  
Divisibility  220  
18.1  Divisibility Test for 2,4 and 8  221  
Test for 2  221  
Test for 4  221  
Test for 8  222  
18.2  Divisibility Test for 3 and 6  222  
Test for 3  222  
Test for 6  223  
18.3  Divisibility Test for 5 and 10  223  
18.4  Divisibility Test for divisor ending in 9  223  
Test for divisor ending in 9  224  
18.5  Divisibility Test for divisor ending in 3  227  
Test of divisor ending in 3  228  
18.6  Divisibility Test divisor ending in 1  231  
Test for divisor ending in 1  231  
18.7  Divisibility Test divisor ending in 7  234  
Test of divisor ending in 7  234  
18.8  Divisibility of Sums and Products  237  
Sample Pages
Back of The Book
What is Vedic Mathematics?
Vedic Mathematics is ancient system of mathematics which was formulated and encapsulated in modern from by jagadguru Swami Bharthi Krishna Tirtha ji. He is the 143rd Shankaracharya of Goverdhan Peeth, Pur. He formulated sixteen sutras and thirteen upasutras. These sutras can be applied effectively in conventional mathematics for faster solutions than the methods usually being.
Why should one know Vedic mathematics?
The solution of the problem can be viewed in different dimensions, providing variety of ways to get the answer which is derived in a simple, fast and accurate manner.
How effective are Vedic math techniques?
Multiplication tables up to 5 are sufficient to solve a problem in Vedic Maths. It has the capability of performing multiple operations at one timeVedic mathematics optimally utilizes both hemispheres of the brain is the seat of language and processes in a logical and sequential order, while the right side is visual(spatial), intuitive, random booting of memory and concentration.
Will it support school curriculum?
The Vedic Maths methods are parallel and supplemental to the school study. It does not confuse the child. Vedic Maths focus is on mastering the core skills that a child needs: to be successful in secondary education and beyond.The course syllabus can be designed dynamically in tandem with the school curriculum. This helps developing the mental abilities of a child. We can custom design Vedic Maths course according to the school academic requirements.
Will Vedic Maths be useful for higher classes?
Yes, concepts such as Quadratic Equations Simulatneous Equations, Trigonometry and even Calculus have been mad simple and easier Vedic mathematics.
Will Vedic Maths help a student to minimize careless mistakes?
In Vedic mathematics the oneline mental formulae have an inbuilt series o verifying methods. Therefore the chance for a wrong answer is minimized.
Shriram M. Chauthaiwale M.Sc. B.Ed working as lecturer in Mathematics since 30 years. He published 3 books on history of mathematics and 1 on Vedic mathematics with CD. 20 odd research papers published in national and international journals and conferences. Numerous articles in news papers and magazines. All india radio talk and Doodarshan T.V. program on Vedic Mathematics since 2008.
Dr. Ramesh completed M.Sc. and Ph.D in Statistics from Indian Agricultural Research Institute, New Delhi. Worked as a Technical consultant for software development for one year, but his fascination for numbers found a creative channel when he joined as the Head of Vedic Mathematics Department, Ved Vignan Maha Vidya Peeth (VVMVP) The Art of Living Foundation in July 2006.
Trained more than 120 teachers in Vedic Mathematics. Taken Vedic Mathematics (classroom and online) courses for national and international participants. Had given talk on Vedic Mathematics in World Space Radio.
In India higher and evolved forms of mathematics were in practice since the Vedic times as well seen through the instances found in the Vedas and related literature.
Swami Bharthi Krisna Tirtha (143rd Shankaracharya of Govardhana Peeth, Puri) derived 16 Sutras and 13 Upasutras which can be universally applied in various disciplines of mathematics. He followed the same tradition while explaining mathematics principles and procedueres.
These Sutras were found to be very effective and enjoyable, with the help of which many mathematics operations ranging from simple additionsubtraction to more difficult topics like Algebra, Differentiation, Integration, Trigonometry an Gemotry can be solved with ease. He gave his methods the name Vedic Mathematics through many misunderstand Vedic Mathematics to being the mathematical concepts enumerated in the Vedas.
The Beauty of Vedic Mathematics is it approaches through simple and direct, single line, nonmonotonic, multichoice, direction independent and faster methods unlike conventional mathematics. This definitely leaves behind wide options in the methodologies to be chosen. Vedic maths ensures a balanced utility of both the right and left brain (logic and creativity respectively). Through Vedic Mathematics the path to infinite wisdom on maths is enjoyable and creative.
Contents

9  
1.1  Numbers and Arithmetic  11  
1.2  Algebra  12  
1.3  Geometry  13  
Intorduction to Vedic Mathematics  17  
2.1  Life and works of Bharati Krishna Teertha Ji  17  
2.2  Art of Living' and Vedic Mathematics  21  
2.3  Advantages of Vedic Mathematics  22  
Sutras  24  
3.1  Meaning of the Sutras  24  
3.2  Sapta Sutrani (Seven Sutras)  27  
3.3  Pancha Upsutrani (Five Upasutra)  29  
3.4  Other UpSutras  31  
Fundamental Concepts  33  
Definations  33  
4.1  Complement of the number (Purakanka)  34  
4.2  Digital Root of the Number  36  
4.3  Vinculum Numbers  37  
4.4  Normal toVinculum Conversion  38  
4.5  Vinculum to Normal Conversion  40  
4.6  Multiplication Tables  40  
Operators  42  
Additon  48  
5.1  Placewise Addition Method  48  
5.2  Addition by Shuddha Method  50  
Subtraction of the Numbers  53  
6.1  Subtraction by Shuddha Method  53  
6.2  Vinculum Subtraction  56  
6.3  Simultaneous Addition and Substraction  58  
Urdhvatiryak Multiplication  60  
7.1  Single Digit Multiplier  61  
7.1.1  1 x 1 Multiplication  61  
7.1.2  2 x 1 Multiplication  61  
7.1.3  3 x 1 Multiplication  63  
7.1.4  4 x 1 Multiplication  64  
7.2  TwoDigit Multiplier  66  
7.2.1  2 x 2 Multiplication  66  
7.2.2  3 x 2 Multiplication  68  
7.2.3  4 x 2 Multiplication  70  
7.3  ThreeDigit Multiplier  71  
7.3.1  3 x 3 Multiplication  71  
7.3.2  4 x 3 Multiplication  73  
7.4  FourDigit Multiplier  75  
7.4.1  4 x 4 Multiplication  75  
7.5  Decimal Number Multiplications  77  
Multiplications  80  
(Some Special Cases)  80  
8.1  Antyayordashke'pi_10 Multiplication  81  
8.2  Antyayordashke'pi_100 Multiplication  84  
8.3  Antyayordashke'pi_1000 Multiplication  86  
8.4  Multiplier is 9,99,999 or 9999  88  
8.4.1  Equal number of digits in multiplicand and Multiplier  88  
8.4.2  Lesser number of digits ni multiplicand  91  
Alogorithim  91  
8.4.3  Multiplicand with grater number of digits  92  
8.5  Multiplication by 11  94  
8.6  Multiplication by 101  96  
8.7  Multiplication by 1001  98  
Sum of Products & Product of Sums  101  
9.1  The Sum of Products: Single digit multiplier  101  
9.2  Sum of Products: Two digit multiplier  104  
9.3  Sum of Products: Three and Four digit multiplier  107  
9.4  Sum of Products of Decimal number  109  
9.5  The Product of Sums and differences  111  
Base Multiplication  116  
10.1  Definitions  
10.2  (a) Near to base 10  118  
10.2  (b) Near to working base m x 10  120  
10.3  (a) Near to base 100  122  
10.3  (b) Near to working base m x 100  123  
10.4  (a) Near to base 1000  124  
10.4  (b) Near to working base m x 1000  126  
10.05  Very near numbers (Nikhilam Method)  127  
Squares  131  
11.1  Anurupyena Method  131  
11.2  Duplex Method  133  
11.2  (a) Square of twodigit number  134  
11.2  (b) Square of threedigit number  136  
11.2  (c) Square of fourdigit number  138  
11.3  Square of the number by Nikhilam method  139  
11.4  Square of Number ending with 5  142  
11.5  Squares of numbers near 50, 500 or 5000  143  
Sum/Products of Squares  146  
12.1  Duplex Method for Sum and Difference of Squares  146  
12.2  Nikhilam Method for Sum and difference of Squares  149  
12.3  Multiplication with squares of a Number  152  
Cubes  156  
13.1  Anurupyena Method for Cube of number  156  
13.2  Sum or Difference of Cubes  159  
13.3  Nikhilam Method for Cube of Number  160  
13.4  Product with Cubes of Two digit Numbe  164  
Dhajanka Division  167  
14.1  Division with Single Digit Divisor  167  
14.2  Division with Two Digit Divisor  170  
14.3  Division with Three Digit Divisor  174  
14.4  Division with Four Digit Divisor  177  
Division of Sums/Products  180  
15.1  Division of Sums  181  
15.2  Division of Product  185  
15.3  Division of Sums of Products  189  
15.4  Division of Product of Sums  192  
15.5  Division of Squares and Cubes  194  
Square Roots of Number  197  
16.1  Facts of Note  197  
16.2  Square Roots by Vilokanam  199  
16.3  Square Roots by Dwandvayoga Method  201  
16.4  Square Roots of Sum or Product of Numbers  250  
16.5  Square Roots of Sums of Squares  208  
Cube Roots  211  
17.1  Facts of Note  211  
17.2  Cube Roots by Vilokanam  213  
17.3  Cube Roots by Division Method  215  
Divisibility  220  
18.1  Divisibility Test for 2,4 and 8  221  
Test for 2  221  
Test for 4  221  
Test for 8  222  
18.2  Divisibility Test for 3 and 6  222  
Test for 3  222  
Test for 6  223  
18.3  Divisibility Test for 5 and 10  223  
18.4  Divisibility Test for divisor ending in 9  223  
Test for divisor ending in 9  224  
18.5  Divisibility Test for divisor ending in 3  227  
Test of divisor ending in 3  228  
18.6  Divisibility Test divisor ending in 1  231  
Test for divisor ending in 1  231  
18.7  Divisibility Test divisor ending in 7  234  
Test of divisor ending in 7  234  
18.8  Divisibility of Sums and Products  237  
Sample Pages