Arithmetic Grade Four

Lesson Ninety-one: Adding Fractions


The step where you might have the most difficulty when adding fractions with unlike denominators is the step where you convert the fractions. Here is a step-by-step example with some explanation for the conversions step. Here's a step-by-step example:


Here are a few examples:


  PROBLEM:  
             3         4     
            ---  +    ---  =
             7         9

  STEP ONE: Find LCD.

            The LCD of 7 and 9 is 63.

  STEP TWO: Convert fractions

            3 x 9       4 x 7             
           -------  +  -------  =          
            7 x 9       9 x 7

   Think: 

         3     ?         4      ?
        --- = ----      --- =  ----
         7     63        9      63

   To change 3/7 to an equivalent fraction with a denominator of 63, you
   must multiply the numerator and denominator by 9. 

   To change 4/9 to an equivalent fraction with a denominator of 63, you
   must multiply the numerator and denominator by 7.

  STEP THREE: Add numerators and leave the denominator alone.

             27          28       55
            ----   +    ----  =  ----
             63          63       63

  STEP FOUR: Reduce if necessary.

             Not necessary in this example.


Here's another example up to the conversion point only.

  PROBLEM:  
             1         1     
            ---  +    ---  =
             3         4

  STEP ONE: Find LCD.

            The LCD of 3 and 4 is 12.

  STEP TWO: Convert fractions

            1 x 4       1 x 3
           -------  +  -------  =
            3 x 4       4 x 3

  Think:

           1      ?         1       ?
          --- =  ----      ---  =  ----
           3      12        4       12

      To convert 1/3 to something over 12 multiply the numerator and 
      denominator by 4.

      To convert 1/4 to something over 12 multiply the numerator and
      denominator by 3.

In the next group of problems you will find the actual answers. (Remember to reduce if necessary.)

Now you get to try a few for yourself.

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