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                 \ 10-Nov-2025  Bharat Arora   Proof-8                                     Reader’s Sign _______________________ Date __________

                example 2. Find 84 ÷ 12.
                Solution.

                Step 1.  8 < 12, so take 84 as the dividend and divide it by 12.
                Step 2.  Recite the multiplication table of 12.                                                7       Q

                           As 7 × 12 = 84, write 7 in the ones place of the quotient and  12                8 4
                           84 below 84.                                                                   –  8 4
                Step 3.  Subtract 84 from 84. We have 84 – 84 = 0 (remainder)                                 0        R

                           So, Q = 7, R = 0.
                Checking:  Quotient × Divisor + Remainder =  Dividend

                                                          7 × 12 + 0 =  84
                                                             84 + 0 =  84
                Therefore, the division is correct.

                Dividing a 3-digit number

                example 3. Divide 574 by 15.
                Solution.

                Step 1.  Since 5 < 15, divide 57 by 15.                                                     3 8        Q
                           Here, 15 goes 3 times (3 × 15 = 45) into 57 with a remainder
                           of 12. Put 3 in the tens place of the quotient and bring                15    5 7 4
                           down the  next  digit  4  alongside  the  remainder  12, to                 –  4 5

                           make it 124.                                                                   1 2 4
                Step 2.  Divide 124 by 15. Here 15 goes 8 times (8 × 15 = 120) into                    –  1 2 0
                           124 with a remainder of 4.                                                         4       R

                           So, Q = 38, R = 4.
                Checking:  Quotient × Divisor + Remainder =  Dividend
                                                         38 × 15 + 4 =  574

                                                            570 + 4 =  574

                Therefore, the division is correct.
                example 4. Divide 145 by 17.
                Solution.

                Step 1.  Since 1 < 17, take 14 as the dividend.
                           But as 14 < 17, take 145 as the dividend.

                Step 2.  Divide 145 by 17.                                                                    8        Q
                           Here, 17  goes 8 times  (8 × 17  = 136) into  145 with a                17     1 4 5
                           remainder of 9. Put 8 in the ones place of the quotient.                    –  1 3 6

                           So, Q = 8, R = 9.                                                                  9       R

                       66        Mathematics 4

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