Contributed by:

This PDF contains :

Abstract:

Keywords:

1. INTRODUCTION,

2. DIFFERENCES IN VEDIC MATHEMATICS & MODERN MATHEMATICS WITH EXAMPLES

3. MAGICAL FORMULA LIKE SHORT TRICKS FOR

MULTIPLICATION ALGORITHM:

4. CONCLUSION

Abstract:

Keywords:

1. INTRODUCTION,

2. DIFFERENCES IN VEDIC MATHEMATICS & MODERN MATHEMATICS WITH EXAMPLES

3. MAGICAL FORMULA LIKE SHORT TRICKS FOR

MULTIPLICATION ALGORITHM:

4. CONCLUSION

1.
International Journal of Engineering Research in Current Trends (IJERCT)

ISSN: 2582-5488, Volume-3 Issue-3, Jun 2021

Difference between Vedic Mathematics and

Modern Mathematics in Multiplication Algorithm

Kavita S. Chauhan, Dr Mohd. Farman Ali

Research Scholar, Department of Basic and Applied Assistant Professor of the Department of Basic and Applied

Science, Madhav University.Rajasthan. Science, Madhav University.Rajasthan.

covered the mathematics such are trigonometry geometry

Abstract: In this paper we are discussed about the methods of algebra Arithmatic physics, calculus – differtial and integral

multiplication formulas in Vedic Mathematics and Modern equations applied mathematics of various kinds dynamics

Mathematics and difference between them. Now the Vedic hydrostatics static kinematics etc.

Mathematics which was come from Vedas in 1911 to 1918 by

Jagadgurushree Bharti Krishna Tirthji in the year of 1884

to1960.By the words of Shree Bharti Krishna Tirthji that our

2. DIFFERENCES OF VEDIC MATHEMATICS &

Mathematics is based on sixteen sutras from Atharva Vedas. It is MODERN MATHEMATICS WITH EXAMPLES:

not use only in arithmetic fundamentals but also use in the

subjects like Science, Engineering, astrology, astronomy etc. The 1) Ekadhikenapurvena: The meaning of this sutra is‟‟ by

formulas of multiplication in Vedic Mathematics is faster than one more than the previous one.‟‟

the formulas of multiplication in Modern Mathematics. We have

to search here the multiplication problems solved from each

sutras of Vedic Mathematics like Ekadhikenapurvena,

Ekanunenapurvena, Triyagbhayam, Antyoyedasake’pi, Nikhilam

Navatskramam Dasatha and Navamguna sutra. It is easy and

more useful for pupils to solve the problems regarding from

multiplication. In other ways there are many converts as magical

formulas like kilometers into meters, meters into kilometers,

Farenheitinto Celcius, kilometers into miles, kilograms into

pounds. So we have faster formulas for converting each magic

calculations. 2) Nikhilamnavatscramamdasataha: This sutra tells us

that„All from 9 and the last from 10‟.

Keywords: Vedic Mathematics, Modern Mathematics, This algorithm for multiplication is more easier, simple

multiplication algorithm, sutras, Ekadhikenapurvena,

Ekanunenapurvena, Navamguna,

and f

Nikhilamnavatscramamdasatha, triyagbhayam, atyoydasake’pi, ast trick for students to solve example like 96×94.

magical formulas, calculation, problems. Here the nearest base is=100.

96 (100-96)

1. INTRODUCTION × 94 (100-94)

Vedic COMES FROM SANSKRIT word “Vedas” its

meaning The fountain head of all knowledge.

Vedic mathematics especially in Europe the beginning of

the 20th century the system of calculation was appeared

when the time in which there was a great interest in ancient

In Sanskrit texts which are called sutras of Ganita which

contains mathematical formulas, each of none find out any

mathematics in that ganita sutras so that they are ignored

now days these types of texts we all known as vadic

mathematics. Therefore result is 96 × 94 = 9024

Now we know about the founder of Vedic mathematics This Example solved by Nikhilam method. It is also

Shree Jag ad Guru Bharti Krishna TirthjiMaharaj who solved by Triyagbhayam and Antyoyedashake‟pi sutra.

discovered the sixteen sutras of mathematics in the periods By Modern mathematics: Here first we take 6×4=24, so

of 1911 to 1918 in this six periods Shree Garuda collected carry=2, then we multiply 9×4=36, now 36+2=38.

those sutras from Atharva Vedas which one known as the 96

ancient Indian system of calculations. Now these sixteen × 94

sutras known as Vedic mathematics. These sutras are 384 → Carry = 2

coming from the Ganit Sutras which are preferred as simple 8640 → Carry = 5

system of mathematics or also known as Shulabh sutras. 9024 → Result

Our ancient culture of Sanskrit that was the sutras which are

dedicated in language of Sanskrit no one understood. Shri Then we take 6×9=54, carry=5, then multiply 9×9=81

Tirthji decoded them in to the more layer of similar sets with .now again summation of 81 and 5 we get total=86. In

various meaning and make them understandable for whole. last step summation of 384 and 8640 we get the last

By research mathematics is based on sixteen sutras or word

-formulas. These sixteen sutras from Vedic texts who

4

ISSN: 2582-5488, Volume-3 Issue-3, Jun 2021

Difference between Vedic Mathematics and

Modern Mathematics in Multiplication Algorithm

Kavita S. Chauhan, Dr Mohd. Farman Ali

Research Scholar, Department of Basic and Applied Assistant Professor of the Department of Basic and Applied

Science, Madhav University.Rajasthan. Science, Madhav University.Rajasthan.

covered the mathematics such are trigonometry geometry

Abstract: In this paper we are discussed about the methods of algebra Arithmatic physics, calculus – differtial and integral

multiplication formulas in Vedic Mathematics and Modern equations applied mathematics of various kinds dynamics

Mathematics and difference between them. Now the Vedic hydrostatics static kinematics etc.

Mathematics which was come from Vedas in 1911 to 1918 by

Jagadgurushree Bharti Krishna Tirthji in the year of 1884

to1960.By the words of Shree Bharti Krishna Tirthji that our

2. DIFFERENCES OF VEDIC MATHEMATICS &

Mathematics is based on sixteen sutras from Atharva Vedas. It is MODERN MATHEMATICS WITH EXAMPLES:

not use only in arithmetic fundamentals but also use in the

subjects like Science, Engineering, astrology, astronomy etc. The 1) Ekadhikenapurvena: The meaning of this sutra is‟‟ by

formulas of multiplication in Vedic Mathematics is faster than one more than the previous one.‟‟

the formulas of multiplication in Modern Mathematics. We have

to search here the multiplication problems solved from each

sutras of Vedic Mathematics like Ekadhikenapurvena,

Ekanunenapurvena, Triyagbhayam, Antyoyedasake’pi, Nikhilam

Navatskramam Dasatha and Navamguna sutra. It is easy and

more useful for pupils to solve the problems regarding from

multiplication. In other ways there are many converts as magical

formulas like kilometers into meters, meters into kilometers,

Farenheitinto Celcius, kilometers into miles, kilograms into

pounds. So we have faster formulas for converting each magic

calculations. 2) Nikhilamnavatscramamdasataha: This sutra tells us

that„All from 9 and the last from 10‟.

Keywords: Vedic Mathematics, Modern Mathematics, This algorithm for multiplication is more easier, simple

multiplication algorithm, sutras, Ekadhikenapurvena,

Ekanunenapurvena, Navamguna,

and f

Nikhilamnavatscramamdasatha, triyagbhayam, atyoydasake’pi, ast trick for students to solve example like 96×94.

magical formulas, calculation, problems. Here the nearest base is=100.

96 (100-96)

1. INTRODUCTION × 94 (100-94)

Vedic COMES FROM SANSKRIT word “Vedas” its

meaning The fountain head of all knowledge.

Vedic mathematics especially in Europe the beginning of

the 20th century the system of calculation was appeared

when the time in which there was a great interest in ancient

In Sanskrit texts which are called sutras of Ganita which

contains mathematical formulas, each of none find out any

mathematics in that ganita sutras so that they are ignored

now days these types of texts we all known as vadic

mathematics. Therefore result is 96 × 94 = 9024

Now we know about the founder of Vedic mathematics This Example solved by Nikhilam method. It is also

Shree Jag ad Guru Bharti Krishna TirthjiMaharaj who solved by Triyagbhayam and Antyoyedashake‟pi sutra.

discovered the sixteen sutras of mathematics in the periods By Modern mathematics: Here first we take 6×4=24, so

of 1911 to 1918 in this six periods Shree Garuda collected carry=2, then we multiply 9×4=36, now 36+2=38.

those sutras from Atharva Vedas which one known as the 96

ancient Indian system of calculations. Now these sixteen × 94

sutras known as Vedic mathematics. These sutras are 384 → Carry = 2

coming from the Ganit Sutras which are preferred as simple 8640 → Carry = 5

system of mathematics or also known as Shulabh sutras. 9024 → Result

Our ancient culture of Sanskrit that was the sutras which are

dedicated in language of Sanskrit no one understood. Shri Then we take 6×9=54, carry=5, then multiply 9×9=81

Tirthji decoded them in to the more layer of similar sets with .now again summation of 81 and 5 we get total=86. In

various meaning and make them understandable for whole. last step summation of 384 and 8640 we get the last

By research mathematics is based on sixteen sutras or word

-formulas. These sixteen sutras from Vedic texts who

4

2.
Difference between Vedic Mathematics and Modern Mathematics in Multiplication Algorithm

result as =9024 which is our required answer. 3) Urdhvatriyagbhayam: The meaning of this sutra is

By Vedic Mathematics: „vertically and cross-wise‟. Here we solve the example

by Vedic Mathematics:

4 2 8 Result = 48 (Because 8 × 6 =48)

× 2 3 6 Pr.carry = 0

8 48

Carry = 4

4 2 8 Result = 36 (Because 12 + 24 = 36)

× 2 3 6 Pr.carry = 4 (By step:1)

0 8 40

Carry = 4

4 2 8 Result = 46 (Because 16 + 24 + 6 = 46)

× 2 3 6 Pr.carry = 4 (By step:2)

0 0 8 50

Carry = 5

4 2 8 Result = 16 (Because 12 + 4 = 16)

× 2 3 6 Pr.carry = 5 (By step:3)

100 8 21

Carry = 2

4 2 8 Result = 08 (Because 4 × 2 = 8)

× 2 3 6 Pr.carry = 2 (By step:4)

101008 10

By Modern Mathematics: Here first we multiply 5) Navamguna sutra: This is the one of the most rule out

428×200=85600, second step multiplication is of three rules in Vedic Mathematics. It is also an

428×30=12840, in third step multiplication is application of Vedic Mathematics. This type of method

428×6=2568, again and again we have done the applied on that number which have one multiplier as 9,

summation of 85600+12840+2568=101008, which is 99, 999…etc.

our required answer. Now we consider an example of this sutra by Vedic

4 2 8 Mathematics: Let us consider 52×9.

× 2 3 6 For calculation the first step is take 9 as (10-1).

8560 In the second step multiply 52 by (10-1).

0 By Modern Mathematics we solve this example as, We

+ 1284 multiply 2 by 9 we get carry=1 then we multiply 5 by 9

0 we get 45 now the summation of 45 and 1 we get 46 in

+ 0256 general by process we get the final answer as 468.

8 5 2

1010 × 9

08 4 6

4) Ekanunenapurvena: The meaning of this sutra is „ by 8

one less than the previous one.‟ Now solve the example Carry = 1, Result = 468

by Vedic Mathematics: Let us consider 32×99.

Now first we take 32 as (32-1) = 31… (a) 6) Antyoyedashake‟pi: This is also one of the rule of

In second step we are going to subtract 99 with the final Vedic Mathematics .In this method „The sum of last

number 99-31=68… (b) two digit of multiplier must be 10.‟

In third step we can say from (a) and (b) that our final We have consider an example of this method by Vedic

answer is 3168. Mathematics: let us consider 54×56.

By Modern Mathematics: Here first we multiply 32× The first step here we see that the sum of last two digit

90=2880, then we multiply 32×9=288. of multiplier is 4+6=10.

3 2 Now take one more digit of 5 which is 6, multiply 5 by

× 9 9 6 we get 30… (a)

2880 Then multiply second digit of first number with second

+ 0288 digit of second number is that 6×4=24 … (b)

3168 So let us join (a) and (b) we get the final result as

Now the summation of 2880 and 288 is 3168 which is

our required answer.

5

result as =9024 which is our required answer. 3) Urdhvatriyagbhayam: The meaning of this sutra is

By Vedic Mathematics: „vertically and cross-wise‟. Here we solve the example

by Vedic Mathematics:

4 2 8 Result = 48 (Because 8 × 6 =48)

× 2 3 6 Pr.carry = 0

8 48

Carry = 4

4 2 8 Result = 36 (Because 12 + 24 = 36)

× 2 3 6 Pr.carry = 4 (By step:1)

0 8 40

Carry = 4

4 2 8 Result = 46 (Because 16 + 24 + 6 = 46)

× 2 3 6 Pr.carry = 4 (By step:2)

0 0 8 50

Carry = 5

4 2 8 Result = 16 (Because 12 + 4 = 16)

× 2 3 6 Pr.carry = 5 (By step:3)

100 8 21

Carry = 2

4 2 8 Result = 08 (Because 4 × 2 = 8)

× 2 3 6 Pr.carry = 2 (By step:4)

101008 10

By Modern Mathematics: Here first we multiply 5) Navamguna sutra: This is the one of the most rule out

428×200=85600, second step multiplication is of three rules in Vedic Mathematics. It is also an

428×30=12840, in third step multiplication is application of Vedic Mathematics. This type of method

428×6=2568, again and again we have done the applied on that number which have one multiplier as 9,

summation of 85600+12840+2568=101008, which is 99, 999…etc.

our required answer. Now we consider an example of this sutra by Vedic

4 2 8 Mathematics: Let us consider 52×9.

× 2 3 6 For calculation the first step is take 9 as (10-1).

8560 In the second step multiply 52 by (10-1).

0 By Modern Mathematics we solve this example as, We

+ 1284 multiply 2 by 9 we get carry=1 then we multiply 5 by 9

0 we get 45 now the summation of 45 and 1 we get 46 in

+ 0256 general by process we get the final answer as 468.

8 5 2

1010 × 9

08 4 6

4) Ekanunenapurvena: The meaning of this sutra is „ by 8

one less than the previous one.‟ Now solve the example Carry = 1, Result = 468

by Vedic Mathematics: Let us consider 32×99.

Now first we take 32 as (32-1) = 31… (a) 6) Antyoyedashake‟pi: This is also one of the rule of

In second step we are going to subtract 99 with the final Vedic Mathematics .In this method „The sum of last

number 99-31=68… (b) two digit of multiplier must be 10.‟

In third step we can say from (a) and (b) that our final We have consider an example of this method by Vedic

answer is 3168. Mathematics: let us consider 54×56.

By Modern Mathematics: Here first we multiply 32× The first step here we see that the sum of last two digit

90=2880, then we multiply 32×9=288. of multiplier is 4+6=10.

3 2 Now take one more digit of 5 which is 6, multiply 5 by

× 9 9 6 we get 30… (a)

2880 Then multiply second digit of first number with second

+ 0288 digit of second number is that 6×4=24 … (b)

3168 So let us join (a) and (b) we get the final result as

Now the summation of 2880 and 288 is 3168 which is

our required answer.

5

3.
International Journal of Engineering Research in Current Trends (IJERCT)

ISSN: 2582-5488, Volume-3 Issue-3, Jun 2021

54×56=3024. mind power, anthuziasm and solving difficult problems in

By Modern Mathematics: any type of exams with high speed and in punctual time with

5 4 accuracy.

× 5 6

270 REFERENCES

0 1. Nitesh Kumar Sharma, Deepesh Kumar Gautam and M. R. Khan,

+ 032 May 2019, Vedic Mathematics Implementation in Multiplier Units,

4 Journal of Computer and Mathematical Sciences, Volume No. 10 (5),

302 Page No.997-1003.

2. Krishna Prasad Karani, January 2016, An Empirical Study on Role of

4 Vedic Mathematics in Improving the speed of Basic Mathematical

(i) In 1st step carry = 2 Operations. International Journal of management, IT and Engineering

(ii) In 2nd step carry = 2 Volume 6 Issue 1 (ISSN: 2249-0558)

(iii) In final result = 3024 3. Dr. Gurjit Kaur and Ms. Harsimranjit Kaur, October 2012, Effect of

Vedic Mathematics on achievement in Mathematics among fifth

grade students. Internation journal of research in education

3. MAGICAL FORMULA LIKE SHORT TRICKS FOR methodology council for innovative research, Volume 1, No. 3 (ISSN:

MULTIPLICATION ALGORITHM: 2278-7690)

4. Dhara R. Joshi, August 2017, Effectiveness of Vedic Mathematics

1) Convert Meters into Centimeters: The formula is 100n. With Multiplication of Nikhilam Sutra o Mathematics Subject In

Let us consider an example: convert 4 meter into Standard 8, International Journal of research in all subjects in multi

languages, Volume 5, Issue 8 (ISSN : 2321-2853)

centimeter we get by formula that 100×4=400.So 4 5. Dr. S. M. Khairnar, Ms. SheetalKapade and Mr.

meter=400centimeters. NareshGhorpade.“Vedic Mathematics the cosmic software fro

2) Convert Centimeters into Meters: The formula is n/100. implementation of fast algorithms”

Let us consider an example: convert 56 centimeters into 6. Archana V. Katgeri “Effectiveness of Vedic Mathematics in the

Classrooms” Volume 4/36, ISSN 2278-8808, Sept-Oct 2017,

meters we get by formula that 56/100=0.56. So 56 Scholarly Research Journal for interdisciplinary Studies.

centimeter = 0.56 meter. 7. Deepshikha Bhargava & Anita Arya “Role of Vedic Mathematics in

3) Convert Fahrenhit into Celcius : The formula is (n- driving optimal solution for real life problems” ISBN 978-93-86171-

30)/2. Where n>30. Let us consider an example: 25-2, (ESHM-17) Jan-2017, International Conference on Recent

Development In Engineering Science Humanities And Management

Convert 36 Fehranheit into Celcius we get by formula National Institute Of Technical Teachers Training And Research

that (36-30)/2= 6/2=3. So 36 Feharnheit= 3 Celcius. Chandigadh, India.

4) Convert Kilos into Pounds: The formula is 22n/10.Let 8. V.K. Gupta. “Vedic Mathematics and the Mathematics of Vedic

us consider an example: Convert 72 kilos into pounds Period – An Analysis and Application, Volume-26, July-December

2015, ISSN 2230-8962.

here we get by formula that(22×72)/10=1584/10=158.4 9. PatilSiddhantVitthal& Dr. Pravin Mane, VeMSC: Apllication of

. So 72 kilos=158.4pounds. Vedic Mathematics for Designing Multipliers, Squarers and Cubers.,

5) Convert kilometers into Miles: The formula is 5n/8. Let Volume-5, Issue 6, November-2019, International Journal of

us consider an example: Convert4 kilometers into miles Engineering and techniques., ISSN 2395-1303

here we get by formula that (5×4)/8=20/8=2.5 .Its

meaning is that 4 kilometers=2.5 miles.

4. CONCLUSION

After going to the concepts of present paper you may see the

difference between Vedic Mathematics and Modern

Mathematics in multiplication algorithm and its applications

are very easy for students for calculating of examples in

their subject of Mathematics, Physics … etc. Here we also

shown the magical formula which are useful for students in

their real life problems and they solved the problems with

this formula.

In the present report we have to consider the 6-sutras which

are the most rules of Vedic Mathematics with applications

and we have suggested this sutras with examples. We have

not proof of the other sutras of Vedic Mathematics but the

basic level of the students maintain level of 4 to 8 standard

students .We summarize this paper. The sutras are also

useful for find out squares, cubes, linear equations,

factorization, Calculus also. In present volume we have

consider short tricks, magical formula, for calculation with

logical improvement has been explained. Here we feel that

present paper can be enjoyed the readers with simple

methods in Vedic Mathematics whenever applying the

methods against the modern methods of the text books. The

reader also compare the differences between both the

methods like Vedic Mathematics and Modern Mathematics.

In general we conclude that the Vedic Mathematics in

multiplication algorithm has more abilities for improving

6

ISSN: 2582-5488, Volume-3 Issue-3, Jun 2021

54×56=3024. mind power, anthuziasm and solving difficult problems in

By Modern Mathematics: any type of exams with high speed and in punctual time with

5 4 accuracy.

× 5 6

270 REFERENCES

0 1. Nitesh Kumar Sharma, Deepesh Kumar Gautam and M. R. Khan,

+ 032 May 2019, Vedic Mathematics Implementation in Multiplier Units,

4 Journal of Computer and Mathematical Sciences, Volume No. 10 (5),

302 Page No.997-1003.

2. Krishna Prasad Karani, January 2016, An Empirical Study on Role of

4 Vedic Mathematics in Improving the speed of Basic Mathematical

(i) In 1st step carry = 2 Operations. International Journal of management, IT and Engineering

(ii) In 2nd step carry = 2 Volume 6 Issue 1 (ISSN: 2249-0558)

(iii) In final result = 3024 3. Dr. Gurjit Kaur and Ms. Harsimranjit Kaur, October 2012, Effect of

Vedic Mathematics on achievement in Mathematics among fifth

grade students. Internation journal of research in education

3. MAGICAL FORMULA LIKE SHORT TRICKS FOR methodology council for innovative research, Volume 1, No. 3 (ISSN:

MULTIPLICATION ALGORITHM: 2278-7690)

4. Dhara R. Joshi, August 2017, Effectiveness of Vedic Mathematics

1) Convert Meters into Centimeters: The formula is 100n. With Multiplication of Nikhilam Sutra o Mathematics Subject In

Let us consider an example: convert 4 meter into Standard 8, International Journal of research in all subjects in multi

languages, Volume 5, Issue 8 (ISSN : 2321-2853)

centimeter we get by formula that 100×4=400.So 4 5. Dr. S. M. Khairnar, Ms. SheetalKapade and Mr.

meter=400centimeters. NareshGhorpade.“Vedic Mathematics the cosmic software fro

2) Convert Centimeters into Meters: The formula is n/100. implementation of fast algorithms”

Let us consider an example: convert 56 centimeters into 6. Archana V. Katgeri “Effectiveness of Vedic Mathematics in the

Classrooms” Volume 4/36, ISSN 2278-8808, Sept-Oct 2017,

meters we get by formula that 56/100=0.56. So 56 Scholarly Research Journal for interdisciplinary Studies.

centimeter = 0.56 meter. 7. Deepshikha Bhargava & Anita Arya “Role of Vedic Mathematics in

3) Convert Fahrenhit into Celcius : The formula is (n- driving optimal solution for real life problems” ISBN 978-93-86171-

30)/2. Where n>30. Let us consider an example: 25-2, (ESHM-17) Jan-2017, International Conference on Recent

Development In Engineering Science Humanities And Management

Convert 36 Fehranheit into Celcius we get by formula National Institute Of Technical Teachers Training And Research

that (36-30)/2= 6/2=3. So 36 Feharnheit= 3 Celcius. Chandigadh, India.

4) Convert Kilos into Pounds: The formula is 22n/10.Let 8. V.K. Gupta. “Vedic Mathematics and the Mathematics of Vedic

us consider an example: Convert 72 kilos into pounds Period – An Analysis and Application, Volume-26, July-December

2015, ISSN 2230-8962.

here we get by formula that(22×72)/10=1584/10=158.4 9. PatilSiddhantVitthal& Dr. Pravin Mane, VeMSC: Apllication of

. So 72 kilos=158.4pounds. Vedic Mathematics for Designing Multipliers, Squarers and Cubers.,

5) Convert kilometers into Miles: The formula is 5n/8. Let Volume-5, Issue 6, November-2019, International Journal of

us consider an example: Convert4 kilometers into miles Engineering and techniques., ISSN 2395-1303

here we get by formula that (5×4)/8=20/8=2.5 .Its

meaning is that 4 kilometers=2.5 miles.

4. CONCLUSION

After going to the concepts of present paper you may see the

difference between Vedic Mathematics and Modern

Mathematics in multiplication algorithm and its applications

are very easy for students for calculating of examples in

their subject of Mathematics, Physics … etc. Here we also

shown the magical formula which are useful for students in

their real life problems and they solved the problems with

this formula.

In the present report we have to consider the 6-sutras which

are the most rules of Vedic Mathematics with applications

and we have suggested this sutras with examples. We have

not proof of the other sutras of Vedic Mathematics but the

basic level of the students maintain level of 4 to 8 standard

students .We summarize this paper. The sutras are also

useful for find out squares, cubes, linear equations,

factorization, Calculus also. In present volume we have

consider short tricks, magical formula, for calculation with

logical improvement has been explained. Here we feel that

present paper can be enjoyed the readers with simple

methods in Vedic Mathematics whenever applying the

methods against the modern methods of the text books. The

reader also compare the differences between both the

methods like Vedic Mathematics and Modern Mathematics.

In general we conclude that the Vedic Mathematics in

multiplication algorithm has more abilities for improving

6