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    E:\Working\Focus_Learning\Math_Genius_3_(11-09-2024)\Open_Files\CHAP_04
                 \ 12-Sep-2024               Surender Prajapati   Proof-5                     Reader’s Sign _______________________ Date __________

                               Step 2:  Multiply 42 by 1 ten.                                    H t O

                                   42 × 1 ten = 420 ones                                             4 2
                                                                                               ×     1 2
                                    Write 420 as the second line product.                            8 4       1st product

                                                                                                  4 2 0       2nd product

                               Step 3:  Add the products obtained in step 1 and                  H t O
                                        step 2.                                                      4 2

                                  84 + 420 = 504                                              ×      1 2
                                                                                                     8 4       1st product
                                            Thus, 42 × 12 = 504.                              + 4 2 0         2nd product
                                                                                                 5 0 4        Sum

                  Example 2: Multiply 56 by 32.

                  Solution:      Expand the multiplier 32 as 3 tens + 2 ones. Now, follow these steps.
                                         Step 1: Multiply 56  Step 2: Multiply 56 by tens. Step 3: Add the products.
                                by 2 ones.                56 × 3 tens = 56 × 30 ones         112 + 1680 = 1792

                                       56 × 2 ones = 112                      = 1680
                                          Write  112  in  1st  Write 1680 in 2nd product
                                 product line.            line.                               th H t O

                                H t O                        th H t O                                5 6
                                   5 6                              5 6                     ×        3 2
                                                                                                   1 1 2
                             ×     3 2                     ×        3 2                     + 1 6 8 0         1st product
                                    1 1 2    1st product          1 1 2       1st product      1 7 9 2        2nd product
                                                                                                              Sum
                                                              1 6 8 0         2nd product

                  Thus, 56 × 32 = 1792.

                  Multiplication of a 3-digit number by a 2-digit number

                  Example 3: Multiply 232 by 23.

                  Solution:   Expand the multiplier 23 as 20 + 3 = 2 tens + 3 ones and multiply 232 with it
                                 by using the following steps:
                                 Step 1:  Multiply 232 by 3 ones.                                          th H t O
                                    232 × 3 ones = 696                                                           2 3 2
                                     Write 696 as first line product.                                   ×           2 3

                                                                                                                 6 9 6
                                 Step 2:  Multiply 232 by 2 tens.                                          th H t O

                                    232 × 2 tens = 232 × 20 ones = 4640 ones                                     2 3 2
                                                                                                        ×           2 3
                                     Write 4640 as second line product.                                          6 9 6

                                                                                                            4    6 4 0

                  Mathematics-3                                                                                          75

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