Formula 3

Anurupyena (आनुरूप्येण)

The upa-Sutra 'Anurupyena' means 'proportionality' or 'similarly'.

अनुपातों से।

इस सूत्र के उपयोग से आनुपातिक गुणन या भाग किया जाता हैं। जब संख्याऐं सैद्धान्तिक आधार 100 से काफी दूर हो तो क्रियात्मक आधार उपयोग में लाया जाता हैं।

This Sutra is highly useful to find products of two numbers when both of them are near the Common bases like 50, 100 etc (multiples of powers of 10).

Example: 47 X 42

As per the previous methods, if we select 100 as base we get

47     -53

42     -58

This is much more difficult. Now by ‘Anurupyena’ we take a different working base through we can solve the problem. Take the nearest higher multiple of 10. In this case it is 50.

Treat it as 100 / 2 = 50.

1.      We choose the working base. Working base is 100 / 2 = 50

2.      Write the numbers one below the other

47

42

__

3.      Write the differences from 50 against each number on right side

47     -03

42     -08

________

4.      Write cross-subtraction or cross- addition as the case may be under the line drawn. Multiply the differences and write the product in the left side of the answer.

5.      Since base is 100 / 2 = 50, 39 in the answer represent 39X50.

Hence divide 39 by 2 (because 50 = 100 / 2). Thus 39 ÷ 2 gives 19½ where 19 is quotient and ½ is remainder. This ½, as Reminder gives 50; making the L.H.S of the answer, 24 + 50 = 74 or (½ x 100 + 28) i.e. R.H.S. 19 and L.H.S. 74 together give the answer 1974.