'Paravartya – Yojayet' means 'transpose and apply'
(i) Consider the division by divisors of more than one digit, and when the
divisors are slightly greater than powers of 10.
Example 1 : Divide 1225 by 12.
Step 1 : (From left to right ) write the Divisor leaving the first digit, write the
other digit or digits using negative (-) sign and place them below the divisor
as shown.
12
-2
‾‾‾‾
Step 2 : Write down the dividend to the right. Set apart the last digit for the
remainder.
42
i.e.,, 12 122 5
- 2
Step 3 : Write the 1st digit below the horizontal line drawn under
thedividend. Multiply the digit by –2, write the product below the 2nd digit
and add.
i.e.,, 12 122 5
-2 -2
‾‾‾‾‾ ‾‾‾‾
10
Since 1 x –2 = -2and 2 + (-2) = 0
Step 4 : We get second digits’ sum as ‘0’. Multiply the second digits’ sum
thus obtained by –2 and writes the product under 3rd digit and add.
12 122 5
- 2 -20
‾‾‾‾ ‾‾‾‾‾‾‾‾‾‾
102 5
Step 5 : Continue the process to the last digit.
i.e., 12 122 5
- 2 -20 -4
‾‾‾‾‾ ‾‾‾‾‾‾‾‾‾‾
102 1
Step 6: The sum of the last digit is the Remainder and the result to its left is
Quotient.
Thus Q = 102 andR = 1
Example 2 : Divide 1697 by 14.
14 1 6 9 7
- 4 -4–8–4
‾‾‾‾ ‾‾‾‾‾‾‾
1 2 1 3
Q = 121, R = 3.
Example 3 : Divide 2598 by 123.
Note that the divisor has 3 digits. So we have to set up the last two
43
digits of the dividend for the remainder.
1 2 3 25 98 Step ( 1 ) & Step ( 2 )
-2-3
‾‾‾‾‾ ‾‾‾‾‾‾‾‾
Now proceed the sequence of steps write –2 and –3 as follows :
1 2 3 25 98
-2-3 -4 -6
‾‾‾‾‾ -2–3
‾‾‾‾‾‾‾‾‾‾
21 1 5
Since 2 X (-2, -3)= -4 , -6;5 – 4 = 1
and (1 X (-2,-3); 9 – 6 – 2 = 1; 8 – 3 = 5.
Hence Q = 21 and R = 15.
