Anurupyena

The upa-Sutra 'anurupyena' means 'proportionality'. This Sutra is highly useful
to find products of two numbers when both of them are near the Common bases
i.e powers of base 10 . It is very clear that in such cases the expected
'Simplicity ' in doing problems is absent.

Example 1: 46 X 43
As per the previous methods, if we select 100 as base we get
46 -54 This is much more difficult and of no use.
43 -57
‾‾‾‾‾‾‾‾
76

Now by ‘anurupyena’ we consider a working base In three ways. We can solve
the problem.
Method 1: Take the nearest higher multiple of 10. In this case it is 50.
Treat it as 100 / 2 = 50. Now the steps are as follows:

i) Choose the working base near to the numbers under consideration.
i.e., working base is 100 / 2 = 50

ii) Write the numbers one below the other
i.e. 4 6
4 3
‾‾‾‾‾‾‾
iii) Write the differences of the two numbers respectively from 50 against each
number on right side
i.e. 46 -04
43 -07
‾‾‾‾‾‾‾‾‾
iv) Write cross-subtraction or cross- addition as the case may be under the line
drawn.

v) Multiply the differences and write the product in the left side of the answer.
46 -04
43 -07
____________
39 / -4 x –7
= 28

vi) Since base is 100 / 2 = 50 , 39 in the answer represents 39X50.
Hence divide 39 by 2 because 50 = 100 / 2
77

Thus 39 ÷ 2 gives 19½ where 19 is quotient and 1 is remainder . This 1 as
Reminder gives one 50 making the L.H.S of the answer 28 + 50 = 78(or
Remainder ½ x 100 + 28 )
i.e. R.H.S 19 and L.H.S 78 together give the answer1978 We represent it as
46 -04
43 -07
‾‾‾‾‾‾‾‾‾
2) 39 / 28
‾‾‾‾‾‾‾‾‾
19½ / 28
= 19 / 78 = 1978