Adding fractions

    2  +  3   =  5
    7      7       7    When fractions have the same denominators just add the numerators
                           and bring over the common denominators.
                           

Sometime we need to add fractions that have different denominators.
For example    1   +   1     This requires that we find a common denominator. Why do we
                         2        3     need to do this. To use an analogy assume that you are going to
                                          add  $3  +  200 pennies. You would change the $3 to 300 pennies
                                          and  add 300 pennies + 200 pennies = 500 pennies or you would
                                          change the 200 pennies to $2 and add $3 + $2 = $5. Either way
                                          you could only get an accurate answer when both quantities
                                          are converted to the same measurement. The same is true with
                                          fractions.

The first step is to find a number that can be divided evenly by 2 and 3. This number is called
a common denominator. If it is the smallest number that can be divided evenly by 2 and 3 we
will call that number the least common denominator (LCD).  The LCD for 2 and 3 is 6.
12, 18, 24 and many others are common denominators but not the LCD. So lets use 6.

    1   =                 What we do is divide the new denominator
    2        6             by the old denominator and multiply the
                             answer by the old numerator. This answer is
 + 1  =                   the new numerator. If you follow this procedure
    3        6              your work will look similar to this  1  =   3
  ------------                                                                      2       6
   
                                                                                       1  =   2
                                                                                   +  3       6
                                                                                      -----------
                                                                                                5
                                                                                                6
Try adding 1/2  +  1/3  using 12 as the common denominator.
Do you get the same answer?    answer
 

Try these examples:
                           1)   1/4  +  1/3  =
                           2)   2/3  +  1/2  =      answer             
 
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