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VEDIC MATHEMATICS : Arithmetic Operations. T. K. Prasad http://www.cs.wright.edu/~tkprasad. 45 * 63 = (4 * 10 + 5) * (6 * 10 + 3) = 4 * 10 * 6 * 10 + 4 * 10 * 3 + 5 * 6 * 10 + 5 * 3. = 4 * 6 * 100 + 4 * 3 * 10

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Vedic mathematics arithmetic operations l.jpg

VEDIC MATHEMATICS : Arithmetic Operations

T. K. Prasad

http://www.cs.wright.edu/~tkprasad

Arithmetic Operations


Multiplying numbers l.jpg

45 * 63

= (4 * 10 + 5)

* (6 * 10 + 3)

= 4 * 10 * 6 * 10

+ 4 * 10 * 3

+ 5 * 6 * 10

+ 5 * 3

= 4 * 6 * 100

+ 4 * 3 * 10

+ 5 * 6* 10

+ 5 * 3

= 24 * 100

+ (12 + 30) * 10

+ 15

Multiplying Numbers

Arithmetic Operations


Multiplying numbers3 l.jpg

= 24 * 100

+ (12 + 30) * 10

+ 15

= 24 * 100

+ 42 * 10

+ 15

= 1 5

1 2 x

3 0 x

2 4 x x

= 2 8 3 5

Multiplying Numbers

Arithmetic Operations


Two digit multiplication of large digits in terms of small digits using vedic approach l.jpg

Two Digit Multiplication (of Large Digits in terms of Small Digits) using Vedic Approach

Method : Vertically and Crosswise Sutra

Correctness and Applicability

Arithmetic Operations


100 s complement l.jpg

Alternatively, 100’s complement of d Digits) using Vedic Approach 1 d2 (d2≠ 0) is (9 - d1) (10 - d2).

HC(35) =

9 10

-3 -5

6 5

HC(11) =

89

HC(35) =

65

HC(94) =

6

100’s Complement

100’s complement of a 2-digit number n is (100 – n).

Arithmetic Operations


Method multiply 79 97 l.jpg
Method: Digits) using Vedic Approach Multiply 79 * 97

  • Write the first number to be multiplied and its 100’s complement in the first row, and the second number to be multiplied and its 100’s complement in the second row.

    79 21

    97 03

Arithmetic Operations


Slide7 l.jpg

79 Digits) using Vedic Approach 21

97 03

  • To determine the 4-digit product:

    • subtractcrosswise to obtain the left digits

      • (79 – 03) = (97 – 21) = 76

    • and

    • multiply the complements vertically to obtain the right digits.

      • (21 * 03) = 63

  • 79 * 97 = 7663

Arithmetic Operations


Another example l.jpg
Another Example Digits) using Vedic Approach

  • 89 * 91 =

  • 89 11

  • 91 09

  • 80 99

  • 89 * 91 = 8099

Arithmetic Operations


Questions l.jpg
Questions Digits) using Vedic Approach

  • Why do both crosswise subtractions yield the same result?

  • Why does this method yield the correct answer for this example?

  • Does this method always work for any pair of digits?

Arithmetic Operations


Proof sketch l.jpg
Proof Sketch Digits) using Vedic Approach

  • (89 – 9) = (91 – 11) = 80

  • Why are they same?

  • (89 – (100 – 91)) = (89 + 91 – 100) = 80

  • (91 – (100 – 89)) = (91 + 89 – 100) = 80

Arithmetic Operations


Correctness of product two possibilities l.jpg

89 = (100 – 11) Digits) using Vedic Approach

91 = (100 – 9)

89 * 91

= 89 * (100 – 9)

= 89 * 100 – (100 – 11) * 9

= 89 * 100 – 100 * 9+ (11 * 9)

= 100 * (89– 9) + 99

= 100 * 80 + 99

= 8099

89 = (100 – 11)

91 = (100 – 9)

89 * 91

= (100 – 11) * 91

= 100 * 91 – 11 * (100 – 9)

= 100 * 91 – 11 * 100 + (11 * 9)

= 100 * (91– 11) + 99

= 100 * 80 + 99

= 8099

Correctness of Product :Two possibilities

Right digit

[Vertical

Product]

Right digit

[Vertical

Product]

Left digit

[Crosswise

Subtraction]

Left digit

[Crosswise

Subtraction]

Arithmetic Operations


Another example12 l.jpg
Another Example Digits) using Vedic Approach

  • 69 * 88

    69 31

    88 12

    57 372

    60 72

  • Note that, the product of the 100’s complements has more than two digits (exceeds 100) . However, the weight associated with 57 and 3 is 100, and hence they can be combined.

Arithmetic Operations


Yet another example l.jpg
Yet Another Example Digits) using Vedic Approach

  • 30 * 21

    30 70

    21 79

    – 49 5530

    – 49+55 30

    6 30

    This approach is validwith suggested modifications but not very useful!

Breakdown?!

Arithmetic Operations


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