Addition and Subtraction of Fractions Adding and Subtracting Fractions With a Common Denominator No matter how tempting it may be, we can only perform addition and subtraction of fractions when the denominators are the same.   When the denominators are the same we just add the numerators Examples   2         1          3         +         =                                     5         5          5    4            6          210          2            +           =             =        Always reduce the answer.                            15          15          315         3   4          5           9              2          +         =           or 1        The result may be improper.                            7          7           7              7   5         1          14           1         -         =             =        We subtract the numerators.                            8         8          28           2 Exercises    6          2                -                                   11        11      Hold mouse over the yellow rectangle for the solution 3         1               +                     4         4          Hold mouse over the yellow rectangle for the solution 7          8                  +                        20        20         Hold mouse over the yellow rectangle for the solution Adding and Subtracting Fractions Without a Common Denominator Now that we know how to add and subtract fractions with a common denominator, what can we do when the denominators are different?  In this case we must first build the fractions so that the denominators are the same.  We first find the LCD and then do the building. Example Add           1          3                          +                               6          8         Solution The common denominator of 6 and 8 is 24, since          6  =  2 x 3     and  8  =  2 x 2 x 2 so that the LCD is         2 x 2 x 2 x 3  =  24 We write           1 x 4          3 x 3            4          9                             +               =           +            We now have the same denominator           6 x 4          8 x 3           24        24                13                =                            24     Example Subtract           3          1                          -                                4         10         Solution The common denominator of 4 and 10 is 20, since          4  =  2 x 2     and  10  =  2  x 5 so that the LCD is         2 x 2 x 5  =  20 We write           3 x 5           1 x 2           15         2                             -                =           -                       4 x 5          10 x 2          20        20                13                =                            20     Example Find the value of x in the equation                  3          2               x  +           =                          7          3 Solution The LCD of 7 and 3 is 21, so that we can write                  3 x 3          2 x 7              x  +                 =                                7 x 3          3 x 7 or                 9            14               x  +             =                             21           21 Since the denominators are the same, the numerators must add up.  Since          5 + 9  =  14                    5               x  =                               21     Exercises Add or subtract.  Simplify the answer.     2         1              +                                  5         9      Hold mouse over the yellow rectangle for the solution 3          1                -                                     4         12      Hold mouse over the yellow rectangle for the solution Application Sierra-At-Tahoe ski resort claims that they just received 3/4 feet of new snow on top of a base of 2/3 feet of snow.  How many total feet of snow does the resort have? Solution We add the two fractions to arrive at the total.           3The LCD of 4 and 3 is 12.                     4          3            4 x 3           3 x 4           9The resort has 1 5/12 feet of snow (one foot five inches of snow).   Back to the Fractions page Back to the Math 187A page Back to the Math Department page e-mail Questions and Suggestions