VEDIC MATHEMATICS Division T K Prasad http www

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VEDIC MATHEMATICS : Division T. K. Prasad http: //www. cs. wright. edu/~tkprasad Prasad Division 1

Division by nine : Examples • • 32 by 9 =3 R 5 32 is the dividend. 9 is the divisor. 3 is the quotient and is also the first digit of the dividend. 5 is the remainder and is also the sum of the two digits of the dividend (5 = 3 +2). Prasad 321 by 9 = 35 R 6 • 3 is the first digit of the quotient and the dividend. • 5 (= 3 +2) is the second digit of the quotient and the sum of the first two digits of the dividend. • 6 (= 5 +1) is the remainder and the sum of the three digits of the dividend. Division 2

Another Example 12311 by 9 1367 R 8 12335 by 9 1369 R … R 14? Correct result: 1370 R 5 Prasad Division 3

Division by nine : Boundary Condition 342 by 9 = 37 R 9 OOPS! = 38 • When remainder is equal to or greater than the divisor, it needs correction. Prasad 346 by 9 = 37 R 13 OOPS! = 38 R 4 • Moral of the Story: Use short-cuts for calculation, but be careful, because they do not work in all cases. Division 4

Justification using long division Prasad Division 5

Crucial Observation Both the quotient and the remainder of dividing a two digit number d 0 by 9 is d. … 80 by 9 = 8 R 8 90 by 9 = 9 R 9 Small OOPS 10 by 9 = 1 R 1 20 by 9 = 2 R 2 30 by 9 = 3 R 3 … 100 by 9 = 10 R 10 OOPS = 11 R 1 Prasad Division 6

Division by nine : More Examples • With this background, you should be able to see why the example in the You. Tube video works and the rationale for the fixes. • http: //www. youtube. com/watch? v=IIwl. Bj. NLpj. I Prasad Division 7

Crucial Observation : Revisited GUESS: The quotient of dividing a two digit number d 0 by 8 is d, and the remainder is 2*d. 10 by 8 = 1 R 2 20 by 8 = 2 R 4 30 by 8 = 3 R 6 40 by 8 = 4 R 8 OOPS =5 R 0 Prasad … 50 by 8 = 6 R 2 60 by 8 = 7 R 4 70 by 8 = 8 R 6 80 by 8 = 9 R 8 OOPS = 10 R 0 90 by 8 = 11 R 2 100 by 8 = 12 R 4 … Division 8

Division by eight : Examples Easy vs Messy 31 by 8 =3 R 7 310 by 8 = 37 R 14 = 38 R 6 • 31 is the dividend. • 8 is the divisor. • 3 is the quotient and is the first digit. • 7 is the remainder and is the sum of the twice of the first digit and the second digit (7 = 2*3 +1). Prasad • 3 is the first digit. • 7 (= 2*3 +1) is the sum of two times the first digit and the second digit. • 14 (= 2*7 +0) is the sum of two times the first two digits and the third digit. Division 9