this book fills a much-needed gap. pioneermathematics secure... · pioneermathematics.com ... what...

Pion

eerM

athe

mat

ics.C

om

Pioneer Education {The Best Way To Success} Medical and Non – Medical Classes

www.pioneermathematics.com S.C.O.- 326, Sector 40–D, Chd. Phone: 9815527721, 4617721

1

"This book fills a much-needed gap."

Pioneer Education

{Medical and Non – Medical Classes} S.C.O. 320 (TF) and 326 Sector 40-D, Chandigarh. Ph: - 9815527721, 4617721

www.pioneermathematics.com

Vedic Mathematics

http://www.pioneermathematics.com/

Pion

eerM

athe

mat

ics.C

om



2

“Vedic mathematics”

“We owe a lot to the Indians, who taught us how to count, without which no

worthwhile scientific discovery could have been made.” Albert Einstein

WHAT IS VEDIC MATHS? The Vedic maths means, the way of doing mathematics in a smarter and shorter way. In India, the oldest

and most knowledge scripture in the form of literature is available and that are known as Vedas which

consists of practical lessons of life and high value teachings. It is the name given to the ancient system of Indian Mathematics which was rediscovered from the Vedas

by Sri Bharati Krishna Tirthaji. According to his research all of mathematics is based on word-formulae.

These formulae describe the way the mind naturally works and are therefore a great help in directing the

student to the appropriate method of solution.

WHY TO LEARN VEDIC?

Since from the ancient times Indians are well enough in maths and give numerous inventions and

contribution to world mathematics. In today’s education system, In India students are not allowed to use

calculators till 12th class (senior secondary schooling) .But their syllabus which is mostly derive and

having patterns of Europe and American education system where student can use calculators, graphers

etc electronic machines after 5th – standard. No doubt foreign students are average has poor solving skills

as compared to Indian students. But Indians students have to face tough challenge while solving complex

calculation specially in 9th & 10th class. In physics numerical like 11th & 12th class In mathematics,

physics, chemistry or Accounts. These lengthy and complex calculations take too much time and create

tremendous pressure during examination with the fear of error. In these kinds of requirements &

situations Vedic (shorter maths) is very helpful. By these tricks a student can save this precious time and

reduce pressure during exams.

The techniques in Vedic Maths are so simple that students of any caliber can learn it with ease.

Moreover, Vedic Maths gives many techniques to do the same calculation and the student has a freedom

of choice while computing.

Students appearing for competitive exams find Vedic Maths as an effective tool in number

crunching when they face a high time-constraint in competitive exams.

Even though we live in the age of electronic devices like calculators & computers, there are many

calculations which become time consuming and sometimes impossible to do using a calculator.

Vedic Maths comes handy for working professionals in their day-to-day activities like a finance

meeting, salary calculations, vendor negotiation etc.

“But the real beauty and effectiveness of Vedic Mathematics cannot be fully appreciated without actually practicing the system. One can then see that it is perhaps the most refined and efficient mathematical system possible.”

Pion

eerM

athe

mat

ics.C

om



3

Index Vedic Mathematics

Square of a number (25-125)

Square root of a number

Cube root of a number

Cube of a number

Percentages and fractions

Vedic multiplication of number of two digits

Square of a number (125-1000)

HCF & LCM

Divisibility of root

Addition

Subtraction

Division

Digital roots

Average

Approximations

Special collection of 9th and 10th questions (Using shortcut techniques)

Pion

eerM

athe

mat

ics.C

om



4

How to learn Vedic Mathematics

{IBM & other MNCs have made it Compulsory}

Squaring of number:

97 is 3 away from 100. So subtract 3 from 97, get 94 (first part of answer). And by

squaring same 3, get 09 (last part of the answer).

To find square of number with 5 as last digit.

Last 2 digits will always be 25 (Last part of the answer) in this case. Just multiply 9 by 10

(9+1 i.e. next digit to 9 in this case) to get 90(First part of answer)

To find square root.

known square unknown squareRequired root known square root

2 known square root

Pion

eerM

athe

mat

ics.C

om



5

To find cube root.

Counting from last we put comma after 9.By seeing the last digit we ascertain that last

digit of cube root will be 1. Now we see 9 and ascertain that 23 = 8 is less than 9 and 33=27

is more. Our first digit thus comes to 2, and the answer is 21.

Vedic Cubing

Take a two digit number say 14.

(i) Find the ratio of the two digits i.e. 1:4

(ii) Now write the cube of the first digit of the number i.e. 13

(iii) Now write numbers in a row of 4 terms in such a way that the first one is the cube of

the first digit and remaining three are obtained in a geometric progression with common

ratio as the ratio of the original two digits

(i.e. 1 : 4) i.e. the row is

(iv) Write twice the values of 2nd and 3rd terms under the terms respectively in second

row. i.e,

(v) Add the numbers column wise and follow carry over process.

This 2744 is nothing but the cube of the number 14

Pion

eerM

athe

mat

ics.C

om



6

Multiplication with digits containing 9’s.

The multiplicand has to be reduced by 1 to obtain L.H.S. of the answer and R.H.S. is

mechanically obtained by the subtraction of L.H.S. from the multiplier.

Multiplication where first figure is same & sum of last digits is 10.

Both numbers here start with 4 and the last figures (2 and 8) add up to 10. Just multiply 4

by 5 (4+1 i.e. next digit to 4 in this case) to get 20 for the first part of the answer. And we

multiply the last figures: 2 x 8 = 16 to get the last part of the answer.

Pion

eerM

athe

mat

ics.C

om



7

Assignment-1(Squares) (1) (86)2 (2)(98)2 (3)(48)2 (4)(53)2 (5)(68)2

(6)(115)2 (7)(120)2 (8) (109)2 (9) (87)2 (10) (76)2

(11) (43)2 (12) (62)2 (13) (71)2 (14) (81)2 (15) (113)2

(16) (123)2 (17) (55)2 (18) (95)2 (19)(88)2 (20) (97)2

(21) (44)2 (22) (102)2 (23) (111)2 (24) (125)2 (25) (65)2

(26) (38)2 (27) (32)2 (28) (59)2 (29) (69)2 (30) (77)2

Pion

eerM

athe

mat

ics.C

om



8

Answers ASSIGNMENT -1

(1) 7396 (2) 9604 (3) 2304 (4) 2809 (5) 4624

(6) 13225 (7) 14400 (8) 11881 (9) 7569 (10) 5776

(11) 1849 (12) 3844 (13) 5041 (14) 6561 (15) 12769

(16) 15129 (17) 3025 (18) 9025 (19) 7744 (20) 9409

(21) 1936 (22) 10404 (23) 12321 (24) 15625 (25) 4225

(26) 1444 (27) 1024 (28) 3481 (29) 4761 (30) 5929

Pion

eerM

athe

mat

ics.C

om



9

Assignment-2(Square Root)

(1) 17 (2) 19 (3) 21 (4) 67 (5) 24

(6) 35 (7) 48 (8) 99 (9) 101 (10) 167

(11) 8 (12) 80 (13) 51 (14) 143 (15) 118

(16) 11 (17) 83 (18) 97 (19) 63 (20) 47

(21) 117 (22) 136 (23) 220 (24) 287 (25) 29

(26) 43 (27) 79 (28) 85 (29) 103 (30) 113

Pion

eerM

athe

mat

ics.C

om



10

Answers

Assignment -2 (1) 4.125 (2)4.375 (3)4.60 (4)8.19

(5)4.90 (6)5.91 (7)6.92 (8)9.94

(9)10.05 (10)12.92 (11)2.82 (12)8.94

(13)7.14 (14)11.95 (15)10.86 (16)3.31

(17)9.11 (18)9.84 (19)7.94 (20)6.86

(21)10.81 (22)11.66 (23)14.83 (24)16.94

(25)5.40 (26)6.56 (27)8.89 (28)9.22

(29)10.15 (30)10.65

Pion

eerM

athe

mat

ics.C

om



11

Assignment-3(Cube Root)

(1) 3 2744 (2) 3 9261 (3) 3 1331 (4) 3 13824 (5) 3 4913

(6) 3 15625 (7) 3 21952 (8) 3 1728 (9) 3 17576 (10) 3 132651

(11) 3 35937 (12) 3 5832 (13) 3 59319 (14) 3 91125 (15) 3 2197

(16) 3 195112 (17) 3 3375 (18) 3 68921 (19) 3 185193 (20) 3 4096

(21) 3 103823 (22) 3 24389 (23) 3 148877 (24) 3 287496 (25) 3 10648

(26) 3 12167 (27) 3 29791 (28) 3 97336 (29) 3 19683 (30) 3 6859

Pion

eerM

athe

mat

ics.C

om



12

Answers Assignment -3 (1) 14 (2)21 (3)11 (4)24 (5) 17

(6)25 (7)28 (8)12 (9)26 (10)51

(11)33 (12)18 (13)39 (14)45 (15)13

(16)58 (17)15 (18)41 (19)57 (20)16

(21)47 (22)29 (23)53 (24)66 (25)22

(26)23 (27)31 (28)46 (29)27 (30)19

Pion

eerM

athe

mat

ics.C

om



13

Assignment-4(Cube of a Number)

(1) 12 (2) 13 (3) 21 (4) 107

(5) 46 (6) 26 (7) 72 (8) 29

(9) 22 (10) 99 (11) 16 (12) 17

(13) 23 (14) 31 (15) 38 (16) 18

(17) 42 (18) 24 (19) 81 (20) 51

(21) 55 (22) 63 (23)49 (24) 11

(25) 74 (26) 14 (27) 87 (28) 20

(29) 15 (30) 39

Pion

eerM

athe

mat

ics.C

om



14

Answers Assignment-4 (1) 1728 (2) 2197 (3) 9261 (4) 1225043

(5) 97336 (6) 17576 (7) 373248 (8) 24389

(9) 10648 (10) 970299 (11) 4096 (12) 4913

(13) 12167 (14) 29791 (15)54872 (16)5832

(17) 74088 (18)13824 (19) 531441 (20) 132651

(21) 166375 (22) 250047 (23)117649 (24)1331

(25) 705224 (26)2744 (27) 658503 (28) 8000

(29)3375 (30) 59319

Pion

eerM

athe

mat

ics.C

om



15

Assignment-5(Multiplication Of Two Numbers Of Two Digits) (1) 72×65 (2) 93×87 (3) 82×71 (4) 73×69 (5) 41×58

(6) 89×99 (7) 82×51 (8) 74×42 (9) 87×75 (10) 23×68

(11) 26×93 (12) 47×43 (13) 63×18 (14) 42×45 (15) 98×97

(16) 11×99 (17) 34×61 (18) 74×64 (19) 85×99 (20) 71×73

(21) 21×69 (22) 73×27 (23) 56×58 (24) 86×72 (25) 40×83

(26) 99×19 (27) 47×63 (28) 27×94 (29) 81×89 (30) 97×61

Pion

eerM

athe

mat

ics.C

om



16

Answers

Assignment -5 (1) 4680 (2) 8091 (3) 5822 (4) 5037 (5) 2378

(6) 8811 (7) 4182 (8) 3108 (9) 6525 (10) 1564

(11) 2418 (12) 2021 (13) 1134 (14) 1890 (15) 9506

(16) 1089 (17) 2074 (18) 4736 (19) 8415 (20) 5183

(21) 1449 (22) 1971 (23) 3248 (24) 6192 (25) 3320

(26) 1881 (27) 2961 (28) 2538 (29) 7209 (30) 5917

Pion

eerM

athe

mat

ics.C

om



17

Assignment-6(Square of a number 125 – 1000)

1. (135)2 2. (538)2 3. (608)2 4. (712)2

5. (814)2 6. (999)2 7. (401)2 8. (336)2

9. (302)2 10. (310)2 11. (305)2 12. (803)2

13. (632)2 14. (779)2 15. (498)2 16. (199)2

17. (191)2 18. (438)2 19. (699)2 20. (784)2

21. (895)2 22. (151)2 23. (172)2 24. (207)2

25. (294)2 26. (550)2 27. (580)2 28. (611)2

29. (306)2 30. (408)2

Pion

eerM

athe

mat

ics.C

om



18

Answers

Assignment-6

1.) 18225 2.) 289444 3.) 369664 4.) 506944

5.) 662596 6.) 998001 7.) 160801 8.) 112896

9.) 91204 10.) 96100 11.) 93025 12.) 644809

13.) 399424 14.) 606841 15.) 248004 16.)39601

17.) 36481 18.) 191844 19.) 488601 20.) 614656

21.) 801025 22.) 22801 23.)29584 24.)42849

25.) 86436 26.) 302500 27.)336400 28.)373321

29.) 93636 30.)166464

For Solutions & Problems visit www.pioneermathematics.

http://www.pioneermathematics/

Pion

eerM

athe

mat

ics.C

om



19

“Testimonials”

Pion

eerM

athe

mat

ics.C

om



20

Courses Offered

Pion

eerM

athe

mat

ics.C

om



21

this book fills a much-needed gap. pioneermathematics secure... · pioneermathematics.com ... what...

Documents