VEDIC MATHEMATICS : Division

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VEDIC MATHEMATICS Division

• T. K. Prasad
• http//www.cs.wright.edu/tkprasad

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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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Another Example

• 12311 by 9
• 1367 R 8
• 12335 by 9
• 1369 R
• R 14?
• Correct result 1370 R 5

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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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Justification using long division
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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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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?vIIwlBjNLpjI

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Crucial Observation Revisited

• GUESS The quotient of dividing a two digit
  number d0 by 8 is d, and the remainder is 2d.
• 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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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 23 1).

• 310 by 8
• 37 R 14
• 38 R 6
• 3 is the first digit.
• 7 ( 23 1) is the sum of two times the first
  digit and the second digit.
• 14 ( 27 0) is the sum of two times the first
  two digits and the third digit.