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    E:\Working\Orange_Education\TouchPad_Maths_4\Open_Files\Chap_03\Chap_03
                 \ 10-Nov-2025  Bharat Arora   Proof-8                                     Reader’s Sign _______________________ Date __________

                Multiplying by any 2-Digit number

                Example 1. Find 48 × 23.
                Solution.
                Step 1.  Multiply by the            Step 2.  Multiply by the            Step 3.  Add the products.
                          ones.                               tens.

                          H T O                              H T O                                   Th  H T O
                             4 8                                 4 8                                         4 8
                      ×      2 3        20 + 3            ×      2 3        20 + 3                 ×         2 3

                          1 4 4         48 × 3                1 4 4                                       1 4 4

                                                          +  9 6 0          48 × 20               +       9 6 0
                                                                                                      1   1 0 4
                Therefore, 48 × 23 = 1104.
                Alternative Method
                                                                                        ×
                Step 1.   Expand each of the two numbers, i.e., 48 into                20        40              8
                           40 and 8, and 23 into 20 and 3.                             3

                Step 2.   Write the expanded form of 48 and 23 along
                           different blocks as shown.                                   ×        40              8
                Step 3.   Multiply 40 and 8 by 20 and write the products               20       800            160
                           as shown.                                                   3

                Step 4.   Multiply 40 and 8 by 3 and write the products                 ×        40              8
                           as shown.                                                   20       800            160
                Step 5.  Now, add the products.                                        3        120             24
                                                                                                920            184
                Therefore, 48 x 23 = 1104.                                                    920 + 184 = 1104

                Example 2. Multiply 532 by 38.

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

                      Th  H T O                        TTh  Th  H T O                            TTh  Th  H T O

                          5 3 2                                5 3 2                                     5 3 2
                   ×          3 8       30 + 8      ×             3 8       30 + 8             ×             3 8
                       4  2 5 6         532 × 8            4   2 5 6                                  4  2 5 6

                                                    +   1  5   9 6 0        532 × 30           +  1   5  9 6 0

                                                                                                  2   0  2 1 6

                Therefore, 532 × 38 = 20216.

                       48        Mathematics 4

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