Paryavarta Yojayet can be translated as “Transpose and Apply.” Transpose refers to exchanging or swapping the positions of two elements. In the context of mathematical operations, it can involve transforming one operation into another.
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For example, subtraction can be transposed into addition in specific formulas.
Transpose and Apply are commonly used when dividing numbers where the divisor is slightly greater than any power of 10 and starts with 1.
Let’s say you want to divide a large number (dividend) by a smaller number (divisor).
Find the complement of the divisor, which means subtracting each digit of the divisor from 9.
For example, if the divisor is 24, its complement would be 75 (9 – 2 = 7 and 9 – 4 = 5).
Divide the dividend by the divisor, ignoring any remainders, and write down the quotient.
Multiply the quotient obtained in step 3 by the complement of the divisor and write down the result.
Subtract the result obtained in step 4 from the dividend, and write down the remainder.
If there are more digits in the dividend, bring down the next digit and repeat steps 3 to 5 until all the numbers have been processed.
The final result will be the concatenation of the quotients obtained in Step 3, and the remainder obtained in Step 5 will be the remainder of the division.
Let’s illustrate this method with an example
Divide 785 by 24.
Complement of 24: 9 – 2 = 7, and 9 – 4 = 5.
So the complement is 75.
Divide 785 by 24: Quotient = 32 (ignore the remainder).
Multiply the quotient by the complement: 32 x 75 = 2400.
Subtract 2400 from 785: 785 – 2400 = -1615 (negative value indicates remainder).
Since we have no more digits in the dividend, the final result is the quotient obtained: 32, and the remainder is -1615.
Therefore, the division of 785 by 24 using the Paravartya Yojayet method gives a quotient of 32 and a remainder of -1615.
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