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                   \ 26-Sep-2025  Bharat Arora   Proof-10                                   Reader’s Sign _______________________ Date __________

                  Multiplication with Regrouping

                  regrouping Ones

                  example 1: Multiply 26 by 3.

                  Solution:  Write the numbers in columns according to their place value and then

                                  multiply.

                   Step 1.   Multiply the ones and regroup. Step 2.  Multiply the tens and add the

                   6 × 3 = 18 ones                           t    O    carried over digit.                      t    O

                             = 1 ten + 8 ones                1         3 × 2 = 6 tens                           1

                   Write 8 in the ones column                2    6    6 tens + 1 ten = 7 tens                  2    6
                                                         ×        3                                         ×        3
                   and carry over 1 to the tens                   8    Write 7 in the tens place.               7    8

                   column.

                   Thus, 26 × 3 = 78.

                  regrouping tens

                  example 2: Multiply 53 by 3.

                  Solution:  Write the numbers in columns according to their place value and then

                                  multiply.

                   Step 1.   Multiply the ones.                        Step 2.  Multiply the tens and regroup.

                   3 × 3 = 9 ones                                      5 × 3 = 15 tens
                   Write 9 in the ones                  H   t    O        = 10 tens + 5 tens                  H    t   O

                   column.                                                = 1 hundred + 5 tens                1
                                                            5    3     Write 5 in the tens column                  5   3
                                                    ×            3     and 1 in the hundreds              ×            3
                                                                 9                                            1    5   9
                                                                       column.

                   Thus, 53 × 3 = 159.

                  regrouping Ones and tens

                  example 3: Multiply 67 by 5.

                  Solution:  Write the numbers in columns according to their place value and then

                                  multiply.

                 104                                                                                    Mathematics-2

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