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    DiviSion by A 1-DiGit numbEr (WitH rEGroupinG)

                Division of a 2-digit number

                Example 1. Divide 78 by 2.

                Solution.

                Step 1.  Arrange the numbers in long division form.                                         t o
                Step 2.  Divide the tens by 2.                                                              3 9      (Q)

                           7 tens ÷ 2 = 3 tens                                                       2      7 8
                           Write 3 in the tens place in the quotient.                                    – 6

                Step 3.  Multiply the divisor and the quotient.                                             1 8

                           3 tens × 2 = 6 tens                                                           – 1 8
                                                                                                               0     (R)
                           Write 6 in the tens place below the dividend.

                           Subtract the digits in the tens column. 7 – 6 = 1

                Step 4.  Bring down 8 ones and regroup with 1 ten. 1 ten + 8 ones = 18 ones.
                Step 5.  Repeat from step 2 to step 3.

                           Divide: 18 ÷ 2 = 9 (Q), Multiply: 2 × 9 = 18, Subtract: 18 – 18 = 0 (R)
                Thus, quotient (Q) = 39, remainder (R) = 0.

                            Checking

                            (Quotient × Divisor) + Remainder = Dividend                      “Dividing a number
                                                      (39 × 2) + 0 = 78                       by itself gives the

                                                            78 + 0 = 78                          quotient 1”.
                            Thus, the division is correct.

                Division of a 3-digit number

                Example 2. Divide 289 by 6.

                Solution.                                                                       Keep in Mind

                Step 1.  Divide the hundreds.                                              When the first digit of the
                           2 cannot be divided by 6.                       t o             dividend  is  smaller than

                           So, regroup hundreds and tens.                  4 8     (Q)     the divisor, we do not put
                           2 hundreds + 8 tens = 28 tens           6    2 8 9              0 in the quotient. Instead,

                Step 2.  Divide 28 tens by 6                          – 2 4                we take the first two digits
                                                                                           together and then divide.
                           28 ÷ 6, quotient = 4 tens                       4 9
                Step 3.  Multiply: 4 × 6 = 24 tens                      – 4 8
                           Subtract: 28 – 24 = 4 tens                         1    (R)

                       100       Mathematics 3

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