Vedic formulas (sutras) propounded by ancient scholars to enrich yours computational skills. By Dr. A. Kumar UPKAR PRAKASHAN, AGRA 2

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2 Vedic formulas (sutras) propounded by ancient scholars to enrich yours computational skills. By Dr. A. Kumar UPKAR PRAKASHAN, AGRA 2

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4 Contents The Vedic Mathematics Sutra 3 Vedic Sutra that makes Arithmetic Computation Easy ,d`kf ds`u iwosz. (Ek adhikena P urvena) 7 2. fuf[ a uor'pjea n'kr# (Nikhilam Navatas'caramam Das'atah) ijkor;z ;kst;srω (Par avartya Yojayet) 12 4.,d`U;wusu iwosz. (Ekany unena P urvena) vkur;ksnz'kds`òfi (Antyayordas'ake'pi) ;konwueω (Y avad unam) ozfr;zx ;keω ( Urdhva-tiryagbhya ~ m) ~ xq.d` leqpp;# leqpp;# xq.d` (Gunakasamuccaya samuccaya gunaka) O;fÆV-lefÆV (Vyasti-Samasti) 53 Vedic Sutra that makes Algebra Easy ijkor;z ;kst;srω (Par avartya Yojayet) lksikur;};eur;eω (Sop antyadvayamantyam) iwj.kiwj.k ;ka (P uranaap urn abhy am) vkuqôi;s 'kwu;aeu;rω ( Anur upye S unyamanyat) lad` u O;od` uk ;keω (Sankalana Vyavakalan abhyam) vk»ek»sukur;eur;su ( Adyam adyen antyamantyena) vur;;ksjso (Antyayoreva) ksialfkkiuk ;keω (Lopanasth apan abhyam) xqf.r leqpp;# leqpp; xqf.r# (Gunitasamuccayah Samuccayagunitah) 'kwu;a lke; leqpp;s (Sunyam S amyasamuccaye) 71

5 Vedic Mathematics Sutra

6 kx.s'k = x. + bz'k (Ganesh) (Gana) (ish) xf.r = x. + brω (Ganit) (Gana) (it) The One meaning of gana x. is numbers. Ganesh x.s'k The lord of numbers, with whose grace schollars perfect intelligence to learn Ganit xf.r to remove the stitching threads of numbers.

7 The Vedic Mathematics Sutra The Vedic mathematics sutra are from Vedas used by our ancient scholars to make mathematical calculations faster, when there were no calculators and computers. These are one line sutras (formulas) or you can say rules with multiple applications. Which not only enrich ones computational skills, but also provide a new way of dealing to the mathematical problem of arithmetic and algebra. For the sake of convenience here the Vedic Mathematics Sutras are divided in two categories : Vedic Sutras that makes arithmetic computation easy and Vedic Sutras that makes algebra easy. Sutras for Arithmetic Computations : These sutras make arithmetic computation like multiplication, division, square, rapid. The sutras and their english translation, that are used here, are as follows :,d`kf ds`u iwosz. (Ek adhikena P urvena) One more than the previous one. fuf[ a uor'pjea n'kr# (Nikhilam Navatas'caramam Das'atah) All from nine last from ten. ozfr;zx ;keω ( Urdhva tiryagbhya ~ m) ~ Vertically and crosswise. ;konwueω (Y avad unam)/whatever the extent of the deficiency. ijkor;z ;kst;srω (Par avartya Yojayet)/Transpose and adjust.,d`u;wusu iwosz. (Ekany unena P urvena)/one less than the previous one. vkur;ksnz'kds`òfi (Antyayordas'ake'pi)/When final digits add upto ten. O;fÆV-lefÆV (Vyasti-Samasti)/Individuality and Totality. xq.d` leqpp;# leqpp;# xq.d` (Gunakasamuccaya samuccayagunaka)/total of expression equals to the total in the product.

8 4 Vedic Math. Sutras For Algebraic Computations : These vedic sutras gives smart solutions to algebraic problems. ijkor;z ;kst;srω (Par avartya Yojayet) Transpose and adjust. lksikur;};eur;eω (Sop antyadvayamantyam)/the ultimate and the twice the penultimate. iwj.kiwj.k ;ka (P urana-ap urn abhy am)/the completion and non-completion. vkuqôi;s 'kwu;aeu;rω ( Anur upye S unyamanyat)/if one in ratio, the other is zero. lad` u O;od` uk ;keω (Sankalana Vyavakalan abhyam)/by addition and subtraction. vk»ek»sukur;eur;su ( Adyam adyen antyamantyena)/the first by first last by last. vur;;ksjso (Antyayoreva)/Only the last term (absolute term). ksialfkkiuk ;keω (Lopanasth apan abhyam)/by Alternate Elimination and Retention. xqf.r leqpp;# leqpp; xqf.r# (Gunitasamuccayah Samuccayagunitah) The product of the sum of the coefficients in the factor is equal to the sum of the coefficients in the product. 'kwu;a lke;leqpp;s (Sunyam S amyasamuccaye) Whenever the expression is the same, that expression is zero.

9 Vedic Sutra that Makes Arithmetic Computation Easy Here we first go with the explanation of vedic sutras, what they mean? And afterward we go with different amazing applications of these vedic sutras in multiplication, square, division, subtraction, squares and square root, cubes and cube roots...

10 ,d`kf ds`u iwosz. (Ek adhikena P urvena) English Translation : One more than previous one (one more than it). Mathematical Meaning : To obtain next number, add one to the previous one. Example : To obtain 2; add one to one; (1 + 1) = 2 To obtain 3; add one to two; (2 + 1) = 3 To obtain 4; add one to three; (3 + 1) = 4 To obtain 5; add one to four; (4 + 1) = 5 To obtain 6; add one to five; (5 + 1) = 6 To obtain 7; add one to six; (6 + 1) = 7 To obtain 8; add one to seven; (7 + 1) = 8 To obtain 9; add one to eight; (8 + 1) = 9 Example : Find the numbers next to 6, 7, 20, 25 respectively. The number next to 6 is (6 + 1) = 7 The number next to 7 is (7 + 1) = 8 The number next to 20 is (20 + 1) = 21 The number next to 25 is (25 + 1) = 26.

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