Understanding Fractions


  1. Definitions

    In module A, all the numbers that we encountered were whole numbers.  Although the whole numbers are important, they only tell part of the story.  Module B is the study of fractions which are defined as parts of the whole.


    Consider the picture below which might represent what is left of a pizza.  We see that the pizza was originally cut into eight slices and there are three slices left.  We say that there is 


    of the pizza remaining.  The number 3 is called the numerator of the fraction and the number 8 is called the denominator of the fraction.  


    Write the fraction of red circles in the diagram below.  


    We see that there are 9 total circles, 5 of which are red.  The total number of circles is the denominator and the number of reds is the numerator:



    1. Use a fraction to represent the shaded part of the whole.

      Hold the mouse over the yellow rectangle for the solution:  5/6

    2. Draw a sketch to illustrate 4/5.


  2. Some Properties of Fractions   

    Recall that there were several properties of division.  Since fractions are really division problems, we arrive at the same properties:

    1. If the numerator and denominator are the same then the fraction equals 1:

                      =  1    

    2. If the denominator is 1 then the fraction is just the numerator

                      =  6    

    3. If the numerator is 0 and the denominator is not 0, then the fraction equals 0

                      =  0    

    4. If the denominator is zero then the fraction is undefined

                        is  undefined   

  3. Applications

    Application of fractions are encountered everywhere.  

    Example    Use a fraction to describe each situation

    1. Out of ten problems on the test you scored nine correct


      You got 9/10 of the problems right 

    2. Of the 75 patrons on Ellie's run, 61 were boarders


      The fraction of boarders on Ellie's run was 61/75

    3. Of the 51 bicycles at your rental shop, you discovered that 8 needed repair.


      8/51 of the bicycles needed repair.

    Exercises  Use a fraction to describe each situation

    1. Of the seven students left in the class, three are women.

      Solution:  3/7 of the students left are women

    2. Seven days of January were snowy.

      Solution:  7/31 of the days in January were snowy

    3. Fifteen of the ninety-one tourists are from Sacramento.

      Solution:  15/91 of the tourists are from Sacramento.



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