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    E:\Working\Focus_Learning\Math_Genius_2_(09-10-2023)\Open_Files\Chap_06
                   \ 17-Nov-2023  Bharat Arora   Proof-5                                    Reader’s Sign _______________________ Date __________

                  Division as Repeated Subtraction on a Number Line

                  example 1: Find 15 ÷ 3 using a number line.
                                                                                                          1 5
                  Solution:  Let us start from 15.                                                        –3           1

                                  Take jumps towards the left. In each jump, cover                        1 2

                                  3 numbers.                                                              –3            2
                                                                                                             9
                                  We take 5 jumps to reach zero.                                          –3           3
                                                                                                             6
                                        5            4            3            2            1             –3            4
                                                                                                             3
                                  0   1   2    3   4   5    6   7   8    9  10 11 12 13 14        15
                                                                                                          –3           5
                                  We also check how many times 3 has been subtracted                         0
                                  from 15.

                                  Clearly, 5 times. Thus, 15 ÷ 3 = 5

                  example 2: Using repeated subtraction on the number line divide 20 by 5.
                  Solution:  Let us start from 20 and take the jumps of 5 each time to reach up to 0.

                                             4                     3                    2                     1

                                  0    1   2   3    4   5   6   7    8   9   10 11 12 13 14       15 16 17 18 19 20
                                         5 – 5 = 0            10 – 5 = 5           15 – 5 = 10           20 – 5 = 15

                                  Here, we see that 4 times 5 has been subtracted from 20 to reach zero.
                                  Thus, 20 ÷ 5 = 4

                          Knowledge Desk
                        l  Subtraction symbol ‘–’ present in ‘÷’ symbol indicates the subtraction process in division.
                        l  Two dots in ‘÷’ symbol are not joined means ‘÷’ symbol is unlike ‘+’ and ‘×’.

                           Practice Time 6C

                  1.  Use repeated subtraction for distributing the following.

                       (a) 14 erasers among 7 children. Each child gets __________ erasers.

                       (b) 12 balls among 3 girls. Each girl gets __________ balls.

                       (c) 36 kites among 6 boys. Each boy gets __________ kites.
                       (d) 20 pencils among 5 students. Each student gets __________ pencils.

                  Mathematics-2                                                                                         117

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