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               \ 30-Sep-2025  Bharat Arora   Proof-9                                 Reader’s Sign _______________________ Date __________






                       Practice time 4D

                Without doing actual division, find the quotient and the remainder.

                1.  78 ÷ 10              2.  420 ÷ 10              3.  936 ÷ 100             4.  2796 ÷ 10
                5.  2365 ÷ 100           6.  23708 ÷ 100           7.  5064 ÷ 1000           8.  2033 ÷ 1000

                9.  13655 ÷ 1000  10.  23009 ÷ 1000               11.  99867 ÷ 1000  12.  101568 ÷ 1000

              estimating the Quotient


              Like multiplication, the rules for rounding off the
              numbers in division remains the same. To estimate                        Challenge Question
              the quotient, we round off the numbers to their                      A number divided by 4 gives

              highest place if a specific round-off is not given.                  a quotient of 123. When the
              Example 1: Estimate the quotient for:                                same number is divided by 3,

                             (a) 1980 ÷ 18.               (b) 24787 ÷ 43           what could the quotient be?

              Solution:  (a)   1980 rounded off to the nearest thousands is 2000.
                                 18 rounded off to the nearest tens is 20.

                                   Estimated quotient                 Actual quotient
                                     20   2000 100                     18   1980 110              Be Aware
                                        –  20                             –  18              If in a division process,
                                           00                                18              only zero(s) are left,
                                        –  00                             –  18              then we add the same
                                             00                                00            number of zeros in the
                                 2000 ÷ 20 = 100                     1980 ÷ 18 = 110         quotient.
                                 The estimated quotient is close to the actual quotient.

                                 So, the answer is reasonable.
                             (b)  24787 ÷ 43

                                   24787 rounded off to the nearest ten thousands place = 20000

                                  43 rounded off to the nearest tens place = 40
                                 Estimated quotient                 Actual quotient

                                   40   20000 500                   43   24787 576
                                      – 200                           –  215
                                           000                            328
                                                                      –   301
                                                                            277
                                                                     –      258
                                  20000 ÷ 40 = 500                           19           24787 ÷ 43 = 576

                                                        (Ignore the remainder, the actual quotient is 576.)
                                 Thus, the estimated quotient is close to the actual quotient.


              Mathematics-4                                                                                          79
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