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PrasadDivision1 VEDIC MATHEMATICS : Division T. K. Prasad http://www.cs.wright.edu/~tkprasad

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PrasadDivision2 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). 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.

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PrasadDivision3 Another Example 12311 by 9 1367 R 8 12335 by 9 1369 R … R 14? Correct result: 1370 R 5

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PrasadDivision4 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. 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.

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PrasadDivision5 Justification using long division

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PrasadDivision6 Crucial Observation Both the quotient and the remainder of dividing a two digit number d0 by 9 is d. 10 by 9 = 1 R 1 20 by 9 = 2 R 2 30 by 9 = 3 R 3 … … 80 by 9 = 8 R 8 90 by 9 = 9 R 9 Small OOPS 100 by 9 = 10 R 10 OOPS = 11 R 1

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PrasadDivision7 Division by nine : More Examples With this background, you should be able to see why the example in the YouTube video works and the rationale for the fixes. http://www.youtube.com/watch?v=IIwlBjNLpjI

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PrasadDivision8 Crucial Observation : Revisited GUESS: The quotient of dividing a two digit number d0 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 … 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 …

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PrasadDivision9 Division by eight : Examples Easy vs Messy 31 by 8 = 3 R 7 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). 310 by 8 = 37 R 14 = 38 R 6 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.

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