Vedic Maths: Anurupyena

Posted by Manish Panchmatia on Tuesday, June 13, 2023 Labels: , ,

Anurupyena

Proportionality

आनुरूप्येण

Any number can be expressed as : N = x + k, Where x is p * (10 ^ n) and k is remainder if you divide N with 10 ^ n. Here N, n, k are integer. k can be negative also. p is decimal number or integer number. p > 1 or p < 1 both are possible. 

Here are the examples:

N

x

k

x = p * (10 ^ n)

p

n

N = (x = p * (10 ^ n) )  + k

41

50

-9

50 = 0.5 * 100

0.5

2

0.5 * ( 10 ^ 2 )  - 9

41

40

+1

40 = 4 * 10

4

1

4 * ( 10 ^ 1 ) + 1

49

50

-1

50 = 0.5 * 100

0.5

2

0.5 * ( 10 ^ 2 ) – 1

249

250

-1

250 = 0.25 * 1000

0.25

3

0.25 * ( 10 ^ 3 ) – 1

245

250

-5

250 = 0.25 * 1000

0.25

3

0.25 * ( 10 ^ 3 ) – 5

229

250

-21

250 = 0.25 * 1000

0.25

3

0.25 * ( 10 ^ 3)  - 21

230

250

-30

250 = 0.25 * 1000

0.25

3

0.25 * ( 10 ^ 3)  - 30

3998

5000

-1002

5000 = 0.5 * 10000

0.5

4

0.5 * ( 10 ^ 4 ) – 1002

4998

5000

-2

5000 = 0.5 * 10000

0.5

4

0.5 * ( 10 ^ 4 ) – 2

532

500

+32

500 = 5 * 100

5

2

5 * ( 10 ^ 2 ) + 32

472

500

-28

500 = 5 * 100

5

2

5 * ( 10 ^ 2 ) – 28

We already know: 

If A = x + a and B = x + b

A * B = x ( x + a + b) + ab 

Now here,

A = px + a and B = px + b

A * B =  (px + a) * (px + b)

=(px) ^ 2 + pxa + pxb + ab

= px (px + a + b) + ab

Here also, a or b or both can be negative or positive.
p > 1 or p < 1 . Both are possible

Example: 
532 * 472 = (5 * 100 + 32) * ( 5 * 100 - 28)

Here A = 532
B = 472
p = 5
n = 2
a = +32
b = -28

As per above formula answer is: px (px + a + b) + ab
= 500 ( 500 + 32 - 28) - 896
= 500 * 504 - 896
= 252000 - 896
= 251104

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