Transcription
www.iskcondesiretree.com
www.iskcondesiretree.com
www.iskcondesiretree.com
www.iskcondesiretree.com
What is Vedic Mathematics ?The “Vedic Mathematics” is called so because of its origin from Vedas. To be morespecific it has originated from “Atharva Vedas” the fourth Veda. “Atharva Veda” dealswith the branches like Engineering, Mathematics, Sculpture, Medicine and all othersciences with which we are today aware of. Vedic Mathematics was rediscovered fromthe Vedas between 1911 and 1918 by Sri Bharati Krsna Tirthaji (1884-1960). According to his research all of mathematics is based on sixteen Sutras or word-formulae andthirteen sub-sutras. For example, ‘Vertically and Crosswise is one of these Sutras.These formulae describe the way the mind naturally works and are therefore a greathelp in directing the student to the appropriate method of solution.Perhaps the most striking feature of the Vedic system is its coherence. Instead of ahotch-potch of unrelated techniques the whole system is beautifully interrelated andunified: the general multiplication method, for example, is easily reversed to allow oneline divisions and the simple squaring method can be reversed to give one-line squareroots. And these are all easily understood. This unifying quality is very satisfying, itmakes mathematics easy and enjoyable and encourages innovation.In the Vedic system ‘difficult’ problems or huge sums can often be solved immediately by the Vedic method. These striking and beautiful methods are just a part of acomplete system of mathematics which is far more systematic than the modern ‘system’. Vedic Mathematics manifests the coherent and unified structure of mathematicsand the methods are complementary, direct and easy.Interest in the Vedic system is growing in education where mathematics teachers arelooking for something better and finding the Vedic system is the answer. Research isbeing carried out in many areas including the effects of learning Vedic Maths on children; developing new, powerful but easy applications of the Vedic Sutras in geometry,calculus, computing etc.But the real beauty and effectiveness of Vedic Mathematics cannot be fully appreciated without actually practising the system. One can then see that it is perhaps the mostrefined and efficient mathematical system possible.1www.iskcondesiretree.comThe simplicity of Vedic Mathematics means that calculations can be carried outmentally (though the methods can also be written down). There are many advantagesin using a flexible, mental system. Pupils can invent their own methods, they are notlimited to the one ‘correct’ method. This leads to more creative, interested and intelligent pupils.
The Sixteen Main Sutras1. By one more than the one before.2. All from 9 and the last from 10.3. Vertically and Cross-wise4. Transpose and Apply5. If the Samuccaya is the Same it is Zero6. If One is in Ratio the Other is Zero7. By Addition and by Subtraction8. By the Completion or Non-Completion9. Differential Calculus10. By the Deficiency11. Specific and General12. The Remainders by the Last Digit13. The Ultimate and Twice the Penultimate15. The Product of the Sum16. All the Multipliers2www.iskcondesiretree.com14. By One Less than the One Before
The Thirteen Sub Sutras1. Proportionately2. The Remainder Remains Constant3. The First by the First and the Last by the Last4. For 7 the Multiplicand is 1435. By Osculation6. Lessen by the Deficiency7. Whatever the Deficiency lessen by that amount andset up the Square of the Deficiency8. Last Totalling 109. Only the Last Terms10. The Sum of the Products11. By Alternative Elimination and Retention12. By Mere Observation3www.iskcondesiretree.com13. The Product of the Sum is the Sum of the Products
1. Mutilpication Base 10 - NikhilamSession I7x 12 9x 13 6x 14 6x 13 8x 18 9x 13 7x 14 6x 16 4www.iskcondesiretree.comC. One number more than 10 and one less than 10
www.iskcondesiretree.com
1. Mutilpication Base 10 - NikhilamSession I7x8 9x8 6x8 6x7 8x8 9x9 7x9 6x6 www.iskcondesiretree.comB. Both numbers less than 10
www.iskcondesiretree.com
1. Mutilpication Base 10 - NikhilamSession I12x 13 14x 12 12x 11 16x 13 17x 14 16x 15 12x 18 14x 16 6www.iskcondesiretree.comA. Both numbers more than 10
www.iskcondesiretree.com
1. Multiplication Base 100 - NikhilamSession II102x 105 104x 102 102x 107 106x 103 109x 104 107x 105 101x 112 104x 106 7www.iskcondesiretree.comA. Both numbers more than 100
www.iskcondesiretree.com
1. Multiplication Base 100 - NikhilamSession II97x 98 99x 98 96x 98 92x 97 94x 95 99x 99 97x 91 96x 92 8www.iskcondesiretree.comB. Both nuumbbers less than 100
www.iskcondesiretree.com
1. Multiplication Base 100 - NikhilamSession II97x 102 99x 103 96x 104 96x 103 99x 104 97x 105 91x 112 94x 106 9www.iskcondesiretree.comC. One number more than 100 and one less than 100
www.iskcondesiretree.com
2. Multiplication Base 50 - NikhilamSession II53x 54 48x 49 51x 55 47x 46 10www.iskcondesiretree.com57x 52
www.iskcondesiretree.com
3. Multiplication Base 20 - NikhilamSession II22x 24 18x 19 21x 26 17x 18 11www.iskcondesiretree.com23x 25
www.iskcondesiretree.com
2. Addition - Dot Method234714565687 3259 457813565889 3321 235678233673 1 5 3 7 589659781456 8782 572189261355 3247 123545682896 2575 986515935628 4298 265764786582 7652 562812545895 1589 12www.iskcondesiretree.comSession III
www.iskcondesiretree.com
2. Addition - Dot Method534717556647 6478 588913566839 3321 535678235638 6 5 3 7 489657783856 8382 172132261335 3244 423533682836 2571 386517935668 4295 365763786522 7651 362812543835 4534 13www.iskcondesiretree.comSession III
www.iskcondesiretree.com
2. Subtraction – Compliment Method100-73 100-42 100-38 100-55 100-22 1000-995 1000-872 1000-795 1000-587 1000-779 10000-8697 10000-8868 14www.iskcondesiretree.comSession IV
www.iskcondesiretree.com
2. Subtraction – Compliment MethodSession IV10000-9897 10000-8897 146-69 132-66 145-69 127-59 12 4- 17 264-39 128-46 297-69 15www.iskcondesiretree.com10000-7589
www.iskcondesiretree.com
2. Subtraction – Compliment Method3532-587 1345- 683 2629- 463 4528- 1658 42432-5918 26321-7808 36457-16998 17042-9531 572122- 488013 526089- 511086 563157-381381 16www.iskcondesiretree.comSession IV
www.iskcondesiretree.com
1. Tables - 10x10Session V17www.iskcondesiretree.comFinger Method
www.iskcondesiretree.com
2. Tables - 20x20Session V18www.iskcondesiretree.comMutilpication Base 10 - Nikhilam
www.iskcondesiretree.com
3. Tables - 20x10Session VMutilpication Base 10 - Nikhilam19www.iskcondesiretree.comBreakup Method
www.iskcondesiretree.com
MutilpicationSession VIA. Numbberss enddingg with 5 - Ekadhikenaa Purvvenaa15x 15 25x 25 105x 105 95x 95 45x 45 115x 115 35x 35 125x 125 205x 205 20www.iskcondesiretree.com65x 65
www.iskcondesiretree.com
MutilpicationSession VIB. Last digits adding to 10 and other digits same - Antayor Daskepi32x 38 21x 29 56x 54 94x 96 121x 129 73x 77 115x 115 91x 99 108x 102 21www.iskcondesiretree.com63x 67
www.iskcondesiretree.com
1. MultiplicationSession VIC. Multiplication by 9,99,999 - Ekanuyena Purvena35x 99 022x 999 0056x 9999 95x 99 125x 999 0738x 9999 115x 999 0912x 9999 0108x 9999 22www.iskcondesiretree.com65x 99
www.iskcondesiretree.com
1. MultiplicationSession VID. Multiplication by 115876x 11 12345x 11 24x 11 239x 11 123x 11 456x 11 654878x 11 999x 11 589765x 11 23www.iskcondesiretree.com54x 11
www.iskcondesiretree.com
1. Multiplication – Urdhva Triyaghyam32x 13 23x 43 55x 63 74x 67 45x 96 34x 56 67x 89 18x 59 54x 75 17x 29 25x 18 31x 42 24www.iskcondesiretree.comSession VII
www.iskcondesiretree.com
1. Multiplication – Urdhva Triyaghyam213x 432 321x 545 516x 153 213x 432 324x 543 513x 152 973x 36 64x 158 972x 42 25www.iskcondesiretree.comSession VII
www.iskcondesiretree.com
2. Mixed Multiplication PracticeSession VII95x95 123x456 21x29 78x999 786x128 86x14 145x11 324x180 787x9999 567x11 26www.iskcondesiretree.com128x122
www.iskcondesiretree.com
2. Mixed Multiplication Practice21x 11 32x 99 51x 59 25x 25 21x 43 324x 11 513x 999 250x 540 0973x 9999 64x 58 72x 78 85x 85 27www.iskcondesiretree.comSession VII
www.iskcondesiretree.com
1. Division – By method of deviationSession VIII44/9 62/9 Q Q Q R R R 27/9 83/9 65/9 Q Q Q R R R 9) 2 7 89) 3 3 99) 2 2 4Q R 9) 4 5 6Q Q R 9) 8 3 2R Q Q R 9) 4 5 6R Q R 28www.iskcondesiretree.com24/9
www.iskcondesiretree.com
1. Division – By method of deviationSession VIIIQ 9) 1 8 7 3R 9) 1 8 5 6 2Q Q 9) 2 5 6 9R 9) 3 4 2 1 0R Q Q 9) 8 7 6 5 2R Q 9) 1 2 3 4 5 69) 8 7 8 2 8 49) 1 5 6 3 2Q Q Q R R R R R 29www.iskcondesiretree.com9) 4 5 6 7
www.iskcondesiretree.com
2. Squares - Yavdunam Tavdunam14x 14 12x 12 15x 15 11x 11 108x 108 103x 103 105x 105 99x 99 22x 22 24x 24 26x 26 27x 27 32x 32 35x 35 205x 205 30www.iskcondesiretree.comSession VIII
www.iskcondesiretree.com
www.iskcondesiretree.com
being carried out in many areas including the effects of learning Vedic Maths on chil-dren; developing new, powerful but easy applications of the Vedic Sutras in geometry, calculus, computing etc. But the real beauty and effectiveness of Vedic Mathematics cannot be fully appreci-ated without actually practising the system. One can then see that it is perhaps the most refined and efficient .
