Arithmetic Grade Four

Lesson Ninety-nine: Adding Fractions

Here's an example of adding up four fractions: 


       2         3        1        3      
      ---   +   ---   +  ---  +  ----  =   
       5         4        2       10      

   FIND LCD:

     5 x 4 = 20
     4 x 5 = 20
     2 x 10 = 20
     10 x 2 = 20

   CONVERT:

      2 x 4       3 x 5       1 x 10       3 x 2
     -------  +  -------  +  --------  +  --------  =
      5 x 4       4 x 5       2 x 20       10 x 2

   ADD:

         8       15       10        6       39
       ----  +  ----  +  ----  +  ----  =  ----
        20       20       20       20       20

   Convert improper fraction 39/20 to mixed number 1 19/20

Here's another example: 


        1       1       1     
       ---  +  ---  +  ----  =
        9       6       12   

    FIND LCD:

        9 x 4 = 36
        6 x 6 = 36
        12 x 3 = 36

     CONVERT FRACTIONS:

       1 x 4      1 x 6       1 x 12
      -------  + -------  +  --------  =
       9 x 4      6 x 6       3 x 12

     ADD:

           4       6     12      22
         ----  + ---- + ---- =  ----
          36      36     36      36

     NOT AN IMPROPER FRACTION, SO NO CONVERSION NEEDED.

     REDUCE:  22/36  = 11/18

Now you get to try a few for yourself. (You only have to solve problems with three fractions.)

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