UPKAR PRAKASHAN, AGRA–2

By

Dr. A. Kumar

Vedic formulas (sutras) propounded byVedic formulas (sutras) propounded byVedic formulas (sutras) propounded byVedic formulas (sutras) propounded byVedic formulas (sutras) propounded byancient scholars to enrich yoursancient scholars to enrich yoursancient scholars to enrich yoursancient scholars to enrich yoursancient scholars to enrich yours

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Code No. 895

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Contents● The Vedic Mathematics Sutra 3Vedic Sutra that makes ArithmeticComputation Easy 5–54

1. ,d`kf|ds`u iwosZ. (Ek–adhikena P–urvena) 7

2. fuf[¥a uor'pjea n'kr#(Nikhilam Navatas'caramam Das'atah) 10

3. ijkoR;Z ;kst;srΩ (Par–avartya Yojayet) 12

4. ,d`U;wusu iwosZ. (Ekany–unena P–urvena) 19

5. vkUR;ksnZ'kds`Òfi (Antyayordas'ake'pi) 21

6. ;konwueΩ (Y–avad–unam) 23

7. ˜÷oZfr;ZX˙;keΩ (~Urdhva-tiryagbhya

~m) 26

8. xq.d` leqPp;# leqPp;# xq.d`(Gunakasamuccaya samuccaya gunaka) 50

9. O;fÆV-lefÆV (Vyasti-Samasti) 53Vedic Sutra that makes Algebra Easy 55–72

10. ijkoR;Z ;kst;srΩ (Par–avartya Yojayet) 56

11. lksikUR;};eUR;eΩ (Sop–antyadvayamantyam) 57

12. iwj.kiwj.k˙;ka (P–uranaap–urn–abhy–am) 58

13. vkuqÔI;s 'kwU;aeU;rΩ (–Anur–upye S–unyamanyat) 60

14. lad`¥u O;od`¥uk˙;keΩ (Sankalana Vyavakalan–abhyam) 62

15. vk»ek»sukUR;eUR;su (–Adyam–adyen–antyamantyena) 64

16. vUR;;ksjso (Antyayoreva) 66

17. ¥ksiaLFkkiuk˙;keΩ (Lopanasth–apan–abhyam) 6818. xqf.r leqPp;# leqPp; xqf.r#

(Gunitasamuccayah Samuccayagunitah) 69

19. 'kwU;a lkE; leqPp;s (Sunyam S–amyasamuccaye) 71

Vedic Mathematics

Sutra

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 graceschollars perfect intelligence to learn Ganit ·xf.r‚ to removethe stitching threads of numbers.

The Vedic Mathematics SutraThe Vedic mathematics sutra are from Vedas used by our

ancient scholars to make mathematical calculations faster, whenthere were no calculators and computers. These are one linesutras (formulas) or you can say rules with multipleapplications. Which not only enrich ones computational skills,but also provide a new way of dealing to the mathematicalproblem of arithmetic and algebra. For the sake of conveniencehere the Vedic Mathematics Sutras are divided in twocategories : Vedic Sutras that makes arithmetic computationeasy and Vedic Sutras that makes algebra easy.

Sutras for Arithmetic Computations : These sutras makearithmetic 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 theprevious one.

● vkUR;ksnZ'kds`Òfi (Antyayordas'ake'pi)/When final digits addupto ten.

● O;fÆV-lefÆV (Vyasti-Samasti)/Individuality and Totality.

● xq.d` leqPp;# leqPp;# xq.d` (Gunakasamuccaya samuccaya-gunaka)/Total of expression equals to the total in theproduct.

4 | Vedic Math.

Sutras For Algebraic Computations : These vedic sutrasgives smart solutions to algebraic problems.

● ijkoR;Z ;kst;srΩ (Par–avartya Yojayet)Transpose and adjust.

● lksikUR;};eUR;eΩ (Sop–antyadvayamantyam)/The ultimate andthe twice the penultimate.

● iwj.kiwj.k˙;ka (P–urana-ap–urn–abhy–am)/The completion andnon-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)/Byaddition 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 AlternateElimination and Retention.

● xqf.r leqPp;# leqPp; xqf.r#(Gunitasamuccayah Samuccayagunitah)The product of the sum of the coefficients in the factor isequal 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 iszero.

Vedic Sutra thatMakes

Arithmetic Computation Easy

Here we first go with the explanation of vedic sutras, whatthey mean ? And afterward we go with different amazingapplications of these vedic sutras in multiplication, square,division, subtraction, squares and square root, cubes and cuberoots.......

,d`kf|ds`u iwosZ.(Ek–adhikena P–urvena)

English Translation : One more than previous one (onemore than it).

Mathematical Meaning : To obtain next number, add oneto 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 respec-tively.

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.