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Office of Academic Services


          DIVISIBILITY RULES FOR FRACTIONS

To reduce a fraction, find a number by which both the numerator and
denominator can be divided.

Divisible evenly by                 If                 Example                Explanation

                            The number ends
         2                       evenly.
                                                        12356                 Ends in 6 (even)


                                                                               1+2+3+6= 12
                         The sum of its digits can
         3                   be divided by 3
                                                         1236                12 can be divided
                                                                                evenly by 3


                          The last two digits can                            32 can be divided
         4                   be divided by 4
                                                         1232
                                                                                evenly by 4


                          The number ends in 0
         5                       or 5
                                                         1235                    Ends in 5


                                                                            1980 can be divided
                           The number can be                                 evenly by 2 and 3;
         6                 divided by 2 and 3
                                                         1980
                                                                          therefore, it is divisible
                                                                                   by 6.
                                                                           The sum of its digits is
                         The sum of its digits can                             3+7+6+2 =18
         9                   be divided by 9
                                                         3762
                                                                             18 can be divided
                                                                                evenly by 9


        10                The number ends in 0          10980                    Ends in 0




Always try dividing by numerator.
              17
Example: In      , both numerator and denominator can be divided by 17.
              51

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5 divisibility rules

  • 1. Office of Academic Services DIVISIBILITY RULES FOR FRACTIONS To reduce a fraction, find a number by which both the numerator and denominator can be divided. Divisible evenly by If Example Explanation The number ends 2 evenly. 12356 Ends in 6 (even) 1+2+3+6= 12 The sum of its digits can 3 be divided by 3 1236 12 can be divided evenly by 3 The last two digits can 32 can be divided 4 be divided by 4 1232 evenly by 4 The number ends in 0 5 or 5 1235 Ends in 5 1980 can be divided The number can be evenly by 2 and 3; 6 divided by 2 and 3 1980 therefore, it is divisible by 6. The sum of its digits is The sum of its digits can 3+7+6+2 =18 9 be divided by 9 3762 18 can be divided evenly by 9 10 The number ends in 0 10980 Ends in 0 Always try dividing by numerator. 17 Example: In , both numerator and denominator can be divided by 17. 51