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Divisibility Rules Worksheet: Reducing Fractions
By Lisa Williams
March 26, 2001

Write true or false.

(1) 3/12 = 1/4  True

(2) 4/10 = 1/2  False

(3) 2/3 = 4/6   True

Reduce these fractions to lowest terms by dividing both terms by the greatest common factor. Greatest common factor means the largest number that is a factor for both numerator and denominator. In 'Mississippiese', it means the biggest number that will go into both top and bottom of the fraction)

 (4) 18/30 18 =  2 x  9  = 2 x 3x 3 30 =  2 x 15 = 2 x 3 x 5 Therefore 2 x 3 = greatest common factor                   6 =  "              "            " so 18/6 = 3      30/6 = 5 when reduced to lowest terms =  3/5 (5) 8/12   8 = 2 x 4 = 2 x 2 x 2  12 = 2 x 6 = 2 x 2 x 3 Therefore 2 x 2 = greatest common factor                   4 =  "             "            "  8/4 = 2 12/4 = 3 reduced to lowest terms = 2/3 (6) 6/24   6 =2 x 3 24 = 2 x 12 = 2 x 2 x 6 = 2 x 2 x 2 x 3 Therefore 2 x 3 = greatest common factor                    6 =    "           "             "  6/6 = 1 24/6 = 4 reduced fraction = 1/4 (7) 5/100  5 = 5 100 = 5 x 20 Therefore  5 = greatest common factor so 5/5 = 1 100/5 = 20 reduced fraction = 1/20 (8) 3/9 3 = 3 9  = 3 x 3  Therefore 3 = greatest common factor so 3/3 = 1 9/3 = 3 reduced terms = 1/3 (9) 12/20 12 = 2 x 6  = 2 x 2 x 3 20 = 2 x 10 = 2 x  2 x 5 Therefore  2 x 2 = greatest common factor                       4 =    "           "           " so 12/4 = 3 20/4 = 5 lowest possible term = 3/5 (10) 12/14 12 = 2 x 6 14 = 2 x 7 Therefore  2 = greatest common factor so  12/2 = 6        14/2 = 7 reduced fraction = 6/7 (11) 30/55 30 = 2 x 15 = 2 x 3 x 5 55 = 5 x 11 Therefore  5 = greatest common factor 30/5 = 6 55/5 = 11 reduced fraction = 6/11   (12) 15/20 15 = 3 x 5  20 = 2 x 10 = 2 x 2 x 5 Therefore   5 = greatest common factor 15/5 = 3 20/5 = 4 reduced fraction term = 3/4 (13) 12/16 12 = 2 x 6 = 2 x 2 x 3  16 = 2 x 8 = 2 x 2 x 4 Therefore 2 x 2 = greatest common factor                        4 =   "          "           " 12/4 = 3 16/4 = 4 reduced fraction = 3/4 (14) 18/27 18 = 2 x 9 = 2 x 3 x 3  27 = 3 x 9 = 3 x 3 x 3  Therefore  3 x 3 = greatest common factor                      9 =     "         "           "  18/9 = 2 27/9 = 3 reduced fraction = 2/3   (15) 54/63 54 = 2 x 27 = 2 x 3 x 9 = 2 x 3 x 3 x 3  63 = 3 x 21 = 3 x 3 x 7 Therefore  3 x 3 = greatest common factor                      9 =   "          "               " 54/9 = 6 63/9 = 7 lowest terms = 6/7 (16) 15/21 15 = 3 x 5  21 = 3 x 7  Therefore 3 = greatest common factor 15/3 = 5 21/3 = 7 lowest terms = 5/7 (17) 6/30   6 = 2 x 3  30 = 2 x 15 = 2 x 3 x 5  Therefore   2 x 3 = greatest common factor                       6 =   "         "          " 6/6 = 1 30/6 = 5 reduced fraction = 1/5 (18) 2/18   2 = 2 18 = 2 x 9 Therefore  2 = greatest common factor so 2/2 = 1 18/2 = 9 lowest terms = 1/9 (19) 4/22   4 = 2 x 2  22 = 2 x 11 Therefore greatest common factor = 2 4/2 = 2 22/2 = 11 reduced fraction = 2/11 (20)12/132   12 = 2 x 6 = 2 x  2 x 3  132 = 2 x 66 = 2 x 2 x 33 = 2 x 2 x 3 x 11 Therefore  2 x 2 x 3 = greatest common factor                          12 =    "       "         " 12/12 = 1 132/12 = 11 therefore 12/132 reduced to its lowest possible terms is 1/11

 Submitted by: Copyright© Lisa Williams I'm a homeschooling mom of 3 elementary school age children. I run a clowning business from my home (Jingles the clown), am pianist for a local church, teach a Sunday School class, teach piano, tutor basic math see Math tutoring and algebra online and I enjoy making people smile.
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