Vedic Mathematics
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The document provides an introduction to Vedic mathematics, which is based on ancient Indian Vedic texts. It describes several Vedic mathematical formulas with examples, such as Ekadhikena Purvena for calculating squares, Nikhilam navatascaramam Dasatah for multiplication involving 9s, and Yavadunam Tavadunikrtya Varganca Yojayet for calculating squares close to bases of powers of 10. Algebraic proofs are also presented for some of the formulas. The document notes that Vedic math techniques can solve difficult math problems with high speed and accuracy, and represents just the beginning of applications of Vedic mathematics.
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- 2. Introduction • Author – Bharati Krishna Tirthaji • Based on Vedas • Vedic Maths
- 3. Ekadhikena Purvena By one more than the previous one Calculate the square of 45.
- 4. Multiply the previous digit by one more than itself 452 = 4X5 and 25 = 2025
- 5. Calculate the square of: • 35 1225 •165 27225
- 6. Algebraic Proof • (ax + b)2 = a2x2 + 2abx + b2 • x=10 and b=5 • (10a + 5)2 = 100a2 + 100a + 25 = 100(a)(a+1) + 25
- 7. Multiplication of two numbers with sum of unit digits=10 and same rest of the number Calculate the product of 67 and 63.
- 8. 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
- 9. Calculate: • 12 X 18 216 • 112 X 118 13216
- 10. 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
- 11. Nikhilam navatascaramam Dasatah All from 9 and the last from 10 Calculate the product of 94 and 97.
- 12. Base – 10, 100, 1000, etc. Deviation – Subtract all from 9 and the last from 10 94 - 6 97 - 3 = 9118
- 13. Calculate: • 98 X 97 9506 • 987 X 990 977130
- 14. Calculate • 14 X 12 168 • 998 X 1025 1023000 – 50 1022950
- 15. 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
- 16. Ekanyunena Purvena One Less than the previous Calculate the product of 15 X 999
- 17. 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
- 18. Calculate: • 64 X 99 6336 • 3251 X 9999 32506749
- 19. 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))
- 20. Yavadunam Tavadunikrtya Varganca Yojayet What ever the deficiency subtract that deficit from the number and write along side the square of that deficit Calculate the square of 96
- 21. 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
- 22. Calculate the squares of: • 994 988036 • 9988 99760144
- 23. 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
- 24. Calculate the square of 476
- 25. 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
- 26. Calculate the square of: • 395 156025 • 68 4624
- 27. Beejank Sum of digits of a number Beejank of 72 = 9, 47 = 1+1 = 2, 68123 = 2+0 = 2 894563912 = 2
- 28. Gunita Samuccayah The 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
- 29. Just The Beginning • Vast scope of Vedic Maths • Solves difficult problems with high speed and accuracy
- 30. THANK YOU