### ĀNURŨPYENA

The upa-Sutra '

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

This is much more difficult and of no use.

Now by ‘Anurupyena’ we consider 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.

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

iii) Write the differences of the two numbers respectively from 50 against each number on right side

iv) 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.

v) Since base is 100 / 2 = 50 , 39 in the answer represents 39X50.

Hence divide 39 by 2 because 50 = 100 / 2

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 answer 1978.

We represent it as

1.46 x 46 2. 57 x 57 3. 54 x 45

*Anurupyena*' means '*proportionality*' or '*similarly*'. This Sutra is highly useful to find products of two numbers when both of them are near the Common bases like 50, 60, 200 etc(multiples of powers of 10).**Example 1: 46 X 43**As per the previous methods, if we select 100 as base we get

This is much more difficult and of no use.

Now by ‘Anurupyena’ we consider 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.

*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

iii) Write the differences of the two numbers respectively from 50 against each number on right side

iv) 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.

v) Since base is 100 / 2 = 50 , 39 in the answer represents 39X50.

Hence divide 39 by 2 because 50 = 100 / 2

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 answer 1978.

We represent it as

**Solve 58 x 48 :****Working base 50 = 5 x 10 gives**

**Find the following products.**1.46 x 46 2. 57 x 57 3. 54 x 45

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