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               \ 30-Sep-2025  Bharat Arora   Proof-9                                        Reader’s Sign _______________________ Date __________





              Let me explain to you how to multiply 2343 by 4.

              Vertical Method                                                                          th H t O

              Step 1:  Multiply 3 ones by 4.                                                                    1

                        3 × 4  = 12 ones = 1 ten 2 ones                                                 2   3 4 3
                        Write 2 in the ones column and carry over 1 to the tens column. ×                           4

              Step 2:  Multiply 4 tens by 4.                                                                        2

                        4 × 4 = 16 tens and 16 tens + 1 ten (carried over)                             th H t O
                        = 17 tens = 1 hundred 7 tens                                                        1   1
                          Write 7 in the tens column and carry over 1 to the                            2   3 4 3
                        hundreds column.                                                             ×              4

              Step 3:  Multiply 3 hundreds by 4.                                                                7 2

                        3 × 4 = 12 hundreds and 12 hundreds + 1 hundred
                        (carried over) = 13 hundreds = 1 thousand + 3 hundreds                         th H t O
                        Write 3 in the hundreds column and carry over 1 to the                          1   1   1

                        thousands column.                                                               2   3 4 3
              Step 4:  Multiply 2 thousands by 4.                                                    ×              4

                        2 × 4 = 8 thousands                                                                 3 7 2
                        and 8 thousands + 1 thousand (carried over) = 9 thousands.

                        Write 9 in the thousands column.                                               th H t O
                                                                                                        1   1   1
                        Thus, 2343 × 4 = 9372.                                                          2   3 4 3
              Horizontal Method                                                                      ×              4


              Step 1: Expand 2343 as: 2343 = 2000 + 300 + 40 + 3                                        9   3 7 2
              Step 2: Multiply each place value by 4.

                            (2000 + 300 + 40 + 3) × 4                                      × 2000 300         40    3

              Step 3: Add the partial products.                                            4 8000 1200 160 12
                        8000 + 1200 + 160 + 12 = 9372

                        Thus, 2343 × 4 = 9372.

              Example 1:  Multiply 1251 × 5.                       Example 2:  Multiply 3263 × 4.
              Solution:             tth th       H    t     O      Solution:             tth th      H     t    O

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

                                ×                           5                       ×                           4
                                            6    2    5     5                             1     3     0    5    2



              Mathematics-4                                                                                          55
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