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    E:\Working\Orange_Education\TouchPad_Maths_4\Open_Files\Chap_08\Chap_08
                     \ 10-Nov-2025  Bharat Arora   Proof-8                                    Reader’s Sign _______________________ Date __________

                    Patterns in multiplication
                    Observe the pattern in the following multiplications.

                        1.   In each multiplication, the last two              2.  The products are the multiples of

                           digits of the product is 25 and the                    105.
                           remaining digits       15  ×  15  =  225                      35  ×  3  ×  1  =  105
                           can be obtained        25  ×  25  =  625                      35  ×  3  ×  2  =  210

                           by multiplying
                           the tens digit of      35  ×  35  =  1225                     35  ×  3  ×  3  =  315
                           a factor with its     ____ × ____ = _____                    ____ × ____ × ____ = _____
                           successor.

                    Fill in the blanks by observing the pattern:

                       3.     1     ×    1     =      1                   4.     9     ×     1     =     9
                             11     ×    11    =     121                         9     ×     11    =     99

                             111    ×   111    =  12321                          9     ×    111    =    999

                            ____  ×  ____  =  ______                            ____  ×  ____  =  _____

                    Patterns in Division

                    We can see many patterns in division. Look at the following pattern and try to fill in

                    the blanks.

                        1.     6    ÷    2     =      3                   2.     10  ÷       5     =      2

                             60  ÷       2     =     30                          100  ÷      5     =     20

                            600  ÷       2     =    300                         1000  ÷      5     =    200
                            ____  ÷  ____  =  _____                             ____  ÷  ____  =  _____

                            ____  ÷  ____  =  _____                             ____  ÷  ____  =  _____

                      3.     111  ÷      3     =    37                    4.
                                                                                                             1
                             222  ÷      6     =    37                           (9 – 1)      ÷  8  =        12
                                                                                 (98 – 2)  ÷  8  =
                             333  ÷      9     =    37
                            ____  ÷  ____  =  ____                               (987 – 3)  ÷  8  =  _____
                                                                                (9876 – 4)  ÷  8  =  _____
                            ____  ÷  ____  =  ____

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                                                                                         Symmetry and Patterns

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