Topic 1 - 1.2  -  Factoring & Fractions

GCF - Greatest Common Factor

LCM  -  Lowest Common Multiiple

Find the GCF & LCM of:     16  &  48

   16  ¸  2   =   6            48   ¸   2  =  24

     8  ¸  2   =   4            24   ¸   2  =  12

     4  ¸  2   =   2            12  ¸    2  =    6

     2  ¸  2   =   1              6  ¸    2  =    3

                                      3  ¸    3  =    1

         2·2·2·2                  2·2·2·2·3

GCF  -  All common factors of both lists raised to the smallest exponent shown in

                any one list.     2·2·2·2  =   16

LCM  -  All different factors in both lists raised to the largest exponent shown in

                any one list.     2·2·2·2·3  =  48

Find the GCF & LCM of:    42  &  105

  42  ¸   2  =  21                105   ¸   3  =  35

  21  ¸   3  =    7                  35  ¸    5  =    7

    7  ¸   7  =    1                    7  ¸    7  =    1

        2·3·7                             3·5·7

GCF  =  3         LCM  =  2·3·5·7  =  210

Find the GCF & LCM of:     24,    46,    &    96

  24  ¸  2  =  12      56  ¸   2  =  28      96  ¸   2  =  48

  12  ¸  2  =    6      28  ¸   2  =  14      48  ¸   2  =  24

    6  ¸  2  =    3      14  ¸   2  =   7       24  ¸   2  =  12

    3  ¸  3  =    1        7  ¸   7  =   1       12  ¸   2  =    6

                                                           6  ¸   2  =    3

                                                           3  ¸   3  =    1

        2·2·2·3              2·2·2·7             2·2·2·2·2·3

GCF  =  2·2·2  =  8    LCM  =  2·2·2·2·2·3·7  =  672 

Fractions

Reduce:

      73/256  =  8·9/8·32  =   9/32

    Factor the numerator and the denominator and cross out the common factors.

Multiplication & Division

   15/28  ·  21/100    =    3/4  ·   3/20    =    9/80 

   Reduce through cross cancellation (reduce through division) and then multiply the 

        numerators and the denominators.

   25/42   ¸    125/24    =    25/42   ·    24/125    =    1/7  ·   4/5    =    4/35   

   Invert the fraction on the right and multiply as in the above problem.

Addition & Subtraction

   8/25    +    11/20   =    32/100    +    55/100    =     87/100

                                LCD  =  100       

   15/16    -    11/24    =    45/48    -    22/48    =    23/48

                                LCD  =  48

   In addition and subtraction of fractions the LCD (Lowest Common Denominator)

     must be determined.  Then raise each fraction to the LCD and add or subtract

     the numerators and keep the LCD.