Explain Sutra Paraavartya Yojayet from vedic maths with example

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Explain Sutra Paraavartya Yojayet from vedic maths with example?

Explain Sutra Paraavartya Yojayet from vedic maths with example?

Answers
Steps 97 ÷ 12
1. Find a Base, that is near the Divisor - that is a power of 10, that is 10n. In this case, the close power of 10 that is nearest to 12 is 10, which is the Base.
2. Find the Transposition of the Divisor - as (Base - Divisor), and represent as Vinculum, if required. Make sure that the Transposition has the same number of digits, as the Zeroes of the Base, 10n In this case, the transposition is:
10 - 12 = -2 = 2
3. Arrange the numbers in a manner, that the Divisor is slightly raised, from its Transposition, and the Dividend on the right-hand side. In this case,
12 2 ) 97
4. Leave some space between the digits of the Dividend, and partition it into 2 parts:
1st Part is for Quotient, and the 2nd Part is for Remainder, such that the digits for the Remainder should be same - as the Zeroes of the Base, 10n. In this case,
12 2 ) 9  |  7
          |
     ---------
5. Drop the first digit (or the cummulative sum of any other number in the same column) of the Dividend, and multiply it (the 'Dropped' digit)with each digits of the Transposition - placing them in rows, next to the place of the 'Dropped' digit. In this case, the first digit is dropped:
12 2 ) 9  |  7
          |
     ---------
       9  |
And, Multiplying the dropped digit, with each digits of the Transposition:
12 2 ) 9  |  7
          | 18
     ---------
       9  |
 
Note: 9 × 2 = 9 × -2 = -18 = 18
5. Drop the next digit (or the cummulative sum of any other number in the same column) of the Dividend, and repeat above step (Step 4) till all the places for every digit of the Dividend is exhausted. In this case, the next digit is dropped:
12 2 ) 9  |  7
          | 18
     ---------
       9  | 11
All places for the digits in the Dividend is exhausted, so we stop.
 
Note: 7 + (-18) = -11 = 11
6. Finalize the Quotient and Remainder parts as:
1. Remove any viniculum number from Quotient;
2. Remove any viniculum number from Remainder;
3. If the Remainder is negative, take appropriate numbers of Quotient to make it positive;
4. If the Remainder is not less than the Dividor, give appropriate numbers to Quotient to make it lesser. In this case,
The Quotient part contains: 9
And, the Remainder part contains: 11 = -11
 
The Remainder is negative. So, we take one from the Quotient: 9 - 1 = 8
And give it to Remainder: 1 × 12 - 11 = 1
 
So, we get: Quotient = 8, and Remainder = 1, which is the answer!

Answerd By:amitoj-singh

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