Arithmetic Grade Four

Lesson Ninety-nine: Adding Fractions

You will recall:

Adding Fractions With Unlike Denominators


Adding more than two fractions with unlike denominators requires that we find an LCD which works for all the denominators in the equation at the same time. Consider this example:

Here's an example: 


       2         3        5          
      ---   +   ---   +  ---   =    
       4         5        6        

      FIND AN LCD for 4, 5, and 6.

        4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60.

        5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60.
 
        6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60.

      NOTICE THAT:

         4 x 15 = 60

         5 x 12 = 60

         6 x 10 = 60

      CONVERT FRACTIONS:

         2 x 15       3 x 12       5 x 10  
        --------  +  --------  +  -------- =
         4 x 15       5 x 12       6 x 10

      SIMPLIFY:

           30       36       50
          ----  +  ----  +  ---- =
           60       60       60

      ADD:

          116
         -----
           60

      Convert improper fraction 116/60 to mixed number 1 56/60

      Remember to reduce (if necessary): 1 56/60 = 1 14/15.

Here's another example: 


        1        5         5        
       ---   +  ---    +  ---  =   
        3        9         6      

     FIND AN LCD for 3, 6, and 9:

       3: 3, 6, 9, 12, 15, 18.

       6: 6, 12, 18.

       9: 9, 18.

     NOTICE THAT:

       3 x 6 = 18

       6 x 3 = 18

       9 x 2 = 18

     CONVERT FRACTIONS:

       1 x 6      5 x 2       5 x 3
      -------  + -------  +  ------- =
       3 x 6      9 x 2       6 x 3

     SIMPLIFY:

           6       10       15
         ----  +  ----  +  ---- =
          18       18       18

     ADD:

            31
           ----
            18

     Convert improper fraction 31/18 to mixed number 1 13/18

     Simplify if necessary:  NOT NECESSARY.

Now you get to try a few for yourself.

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