Arithmetic Grade Four

Lesson Ninety-three: Subtracting Fractions


The step where you might have the most difficulty when subtracting fractions with unlike denominators is the step where you convert the fractions. Here is a step-by-step example with some explanation for the conversion step.



  PROBLEM:  
             4         4     
            ---   -   ---  =
             7         9

  STEP ONE: Find LCD.

            The LCD of 7 and 9 is 63.

  STEP TWO: Convert fractions

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

   Think: 

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

   To change 4/7 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: Subtract numerators and leave the denominator alone.

             36          28       8
            ----   -    ----  =  ----
             63          63       63

  STEP FOUR: Reduce if necessary.

             Not necessary in this example.


Here's another example:

  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.

  STEP THREE: Subtract numerators and leave denominators alone.

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

In the next group of problems you will solve several of these problems. (Remember to reduce if necessary.)

Now you get to try a few for yourself.

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