Tutorial 9

(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.

            i.e.,,     12     122     5
                      - 2

Step 3 : Write the 1st digit below the horizontal line drawn under the dividend. 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 = -2 and 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 and R = 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 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             2 5     9 8
                                    -2-3              -4    -6
                                   ―――――                   -2–3
                                                      ――――――――――
                                                       2 1     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.

Example 4 : Divide 239479 by 11213. The divisor has 5 digits. So the last 4 digits of the dividend are to be set up for Remainder.

                            1 1 2 1 3         2 3     9  4 7 9
                           -1-2-1-3           -2    -4-2-6         with 2
                           ――――――――                 -1-2-1-3      with 1
                                                 ―――――――――――――
                                                  2 1      4 0 0 6

                            Hence Q = 21, R = 4006.

Example 5 :  Divide   13456 by 1123

                            1 1 2  3             1 3 4  5         6
                             -1–2–3              -1-2-3
                            ―――――――                -2-4       –6
                                                    ―――――――――――――
                                                    1 2 0–2        0

Note that the remainder portion contains –20, i.e.,, a negative quantity. To over come this situation, take 1 over from the quotient column, i.e.,, 1123 over to the right side, subtract the remainder portion 20 to get the actual remainder.

Thus Q = 12 – 1 = 11, and R = 1123 - 20 = 1103.