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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 __________

                      4.  Grouping property: The product of three numbers does not change when we
                           change how the numbers are grouped.
                           Example: 20 × (6 × 5) = 20 × 30 = 600                same

                                        (20 × 6) × 5 = 120 × 5  = 600
                           So,          20 × (6 × 5) = (20 × 6) × 5.

                                                                                                    21 st
                              Activity                                                            Century   #Computational Thinking
                                                                                                   Skills

                       To explore multiplication and look for patterns in numbers:

                       Multiply 76923 by 1, 10, 9, 12, 3 and 4.
                            76923 × 1 = 076923              76923 × 10 = 769230              76923 × 9 = 692307

                           76923 × 12 = ___________          76923 × 3 = ___________         76923 × 4 = ___________
                       Do you see any pattern in the result obtained? ___________

                       Discuss the digits that appear in the product in each case.

                                Exercise 3A

                        1.  Fill in the blanks.

                           a.  123 × 1 = _____                              b.  167 × _____ = 167

                           c.  _____ × 1 = 572                              d.  3241 × _____ = 0
                           e.  457 × 0 = _____                               f.  953 × _____ = 0

                           g.  48 × 165 = 165 × _____                       h.  432 × 522 = _____ × 432

                            i.  169 × _____ = 215 × 169                      j.  12 × (16 × 19) = (12 × _____) × 19

                           k.  62 × ( _____ × 49) = (62 × 93) × 49

                       2.  Match the following multiplication sums with their properties.

                                      Column A                                               Column B

                           a.   3 × (4 × 6) = (3 × 4) × 6                       i. Multiplicative property of 1
                           b. 16 × 0 = 0 × 16 = 0                              ii. Grouping property of multiplication

                           c.   24 × 1 = 1 × 24 = 24                           iii. Order property of multiplication

                           d. 3 × 6 = 6 × 3 = 18                              iv. Multiplicative property of 0

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                                                                                                 Multiplication

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