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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 Numbers Arranged in a Shape                                           Century
                                                                                                    21 st
                                                                                                   Skills  #Critical Thinking
                Numbers can be  arranged to  form a shape  or fit
                inside  a shape.  These numbers  can also have
                patterns.  Here are some numbers that  have been                               3           45
                arranged as a rectangle.                                               9                          37
                example. Find the missing number.                                                6       8

                Solution.  On observing the  figure closely, we find                  18         7       ?        45
                that  each number in the smaller rectangle is the
                difference of the two numbers outside it.                                     11           54
                Now, we will observe these parts individually.

                                                                                       7             ?
                                3                  45                       18                                 45

                        9                                 37                        11                54
                                   6            8

                Hence, the missing number = 54 – 45 = 9.

                            Exercise 8D

                    1.  Find the pattern in each of the following and fill in the missing numbers:
                        a.  1, 4, 7, 10, 13, _____, _____, _____, _____

                        b.  512, 256, 128, _____, _____, _____, _____

                    2.  Study the pattern and fill in the missing numbers:

                        a.                             b.                                  c.
                                   21    15                          ?      36                         7     5
                                                               32                 48
                                ?            9                                                    2    9    18   13
                                                               12                 8
                                3            8                                                    11    ?   37   22
                                                                     9       5
                                    5    7                                                            19    15

                    3.  Study the pattern and write the next two steps.
                        a.       1 × 8 + 1 = 9         b.      0 × 9 + 1 = 1               c.      0 × 9 + 8 = 8

                                12 × 8 + 2 = 98                 1 × 9 + 2 = 11                      9 × 9 + 7 = 88

                               123 × 8 + 3 = 987               12 × 9 + 3 = 111                    98 × 9 + 6 = 888

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