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.
   
   Example
   
   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 
   
           3
                       
           8  
   
   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.  
   
   
   Example
   
   Write the fraction of red circles in the diagram below.  
   
   
   Solution
   
   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:
   
           5
                       
           9
   
   Exercise
   

   1. Use a fraction to represent the shaded part of the whole.
      
      
      
      Hold the mouse over the yellow rectangle for the solution: 
      
      

   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:
      
              4
                      =  1    
              4
      
      

   2. If the denominator is 1 then the fraction is just the numerator
      
              6
                      =  6    
              1
      

   3. If the numerator is 0 and the denominator is not 0, then the fraction equals 0
      
              0
                      =  0    
              9
      
      

   4. If the denominator is zero then the fraction is undefined
      
              2
                        is  undefined   
              0
      
      

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
      
      Solution:  
      
      You got 9/10 of the problems right 
      
      

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

   2. Seven days of January were snowy.
      
      Solution: 
      
      
      
      

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

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