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# Proportionality or Similarity

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This sutra is highly helpful in finding the products of two numbers when both of them are near the common base like 30,40,50...200 etc ..(i.e : the multiples of powers of 10 )
Example 1:
46 * 41 =?
Here,note that the above numbers are near to the base 50.So subtracting them from their base,we get
46 (-4)
41 (-9)
-------
(46-9) or (41-4) | (4* 9)
=37 | 36
Divide  37 them by half since we consider base 100/2 =50, so we get L.H.S as
37/2= 18.5 where 18 is the quotient and 1 is the remainder.This remainder 1 gives us one more 50 to be added to the R.H.S,so we get,
36+50 =86
Combining the two L.H.S and R.H.S,we get
=18|86
=1886
Result: 46 * 41= 1886

Lets try taking a different number
Example 2:
37 * 39 = ?
Look here,the above numbers are near to number 40.Also 100/2.5= 40
37  (-3)
39  (-1)
-------------
(37 - 1) or (39 -1) | 3 *1
= 36 |3.......Now 36 /2.5 = 14.4 where 14 is our answer on L.H.S and the 4 is remainder.It is taken as 40 and is added to the R.H.S,so we get 40+3=43
Combining both sides,
=14|43
=1443
Result :37 * 39=1443

Again let me try another one
Example 3:
52 * 43 = ?
The above two numbers are near to base 50.ALSO 100/2=50
52  (+2)
43  (-7)
------------
(52-7) or (43+2) | 2*(-7)
= 45 | (-14)
= (45 /2)| (-14)
= 22.5 | (-14)....where 22 is our quotient and 5 is our remainder.We assume 5 as 50 and add to our R.H.S
= 22 | (50 -14)
=22 | 36
=2236
Result : 52 * 43 =2236

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