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    example 2. Multiply 232 by 23.

                    Solution. Here, the multiplier 23 = 2 tens + 3 ones = 20 + 3. So, we multiply 232 by 23

                    stepwise as shown below.

                    Step 1. Multiply 232                Step 2.  Multiply 232               Step 3.  Add the partial
                              by the ones.                        by the tens.                        products.

                                                                                                          Th H      T O

                                                                       Th H      T O                            2   3    2

                                   Th H      T O                             2   3    2                ×            2    3

                                         2   3    2                 ×            2    3                         6   9   6
                                ×            2    3                          6   9   6                 +   4    6   4   0

                                         6   9   6                      4    6   4   0                     5    3   3   6

                              232 × 3 = 696                       232 × 20 = 4640                 696 + 4640 = 5336

                    So, 232 × 23 = 5336.

                    Multiplication of a 2- and 3-digit Number by a 2-digit Number (With regrouping)

                    example 3. Multiply 56 by 32.

                    Solution.  Here, multiplier  32 = 3 tens + 2 ones  = 30 + 2. So, we multiply  56 by  32
                    stepwise as shown below.

                    Step 1. Multiply 56                 Step 2.  Multiply 56                Step 3.  Add the partial
                              by the ones.                        by the tens.                        products.

                                                                       Th H      T O                      Th H      T O
                                                                                                                    5   6
                                    H    T O                             1   1

                                     1   1                                       5   6                ×             3   2
                                         5   6                      ×            3    2                         1   1   2

                                ×        3   2                               1   1    2                +   1   6    8   0

                                    1    1   2                          1    6   8   0                     1    7   9   2

                              56 × 2 = 112                        56 × 30 = 1680                      112 + 1680 = 1792

                    So, 56 × 32 = 1792.

                                                                                                                  79
                                                                                                 Multiplication

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