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    E:\Working\Focus_Learning\Math_Genius_3_(11-09-2024)\Open_Files\CHAP_05
                 \ 12-Sep-2024                      Surender Prajapati   Proof-5              Reader’s Sign _______________________ Date __________

                  propErtiEs of Division

                  1.  division of a number by 1: When a number is divided by 1, the quotient is the number
                       itself.

                       examples:        (a) 5 ÷ 1 = 5        (b) 10 ÷ 1 = 10       (c) 28 ÷ 1 = 28

                  2.  division of a number by itself: When a number is divided by itself, the quotient is 1.

                       examples:        (a) 12 ÷ 12 = 1      (b) 26 ÷ 26 = 1       (c) 64 ÷ 64 = 1

                  3.  division of zero by any number: When 0 is divided by any number (except 0) gives

                       the quotient 0.
                                                                                                        Note
                       example: 0 ÷ 14 = 0                                                   Division of any number by 0
                                                                                             is not defined. That is, 15 ÷
                                                                                             0 = Not defined.
                  long Division

                  We have learnt to express a division fact like 15 ÷ 3 = 5 as  3 15            5
                                                                                           15
                                                                                             0

                                                         long Division

                           Without remainder                                            With remainder

                               Quotient        example:                           Quotient          example:
                       Divisor Dividend       3 6     2                  Divisor Dividend           4 9     2
                                                  6                                                     8
                                                  0                              Remainder              1

                  Here, we can see that 2 × 3 + 0 = 6

                                           2 × 4 + 1 = 9

                  That means, Quotient × Divisor + Remainder = Dividend

                  When the given number of things cannot be shared equally and something is left over,
                  the leftover is called the remainder.

                  checking Division

                  Division can be checked by using the following relation.
                  Quotient × Divisor + Remainder = Dividend

                  90                                                                                    Mathematics-3

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