Understanding Fractions   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 Use a fraction to represent the shaded part of the whole. Hold the mouse over the yellow rectangle for the solution:  Draw a sketch to illustrate 4/5.   Some Properties of Fractions    Recall that there were several properties of division.  Since fractions are really division problems, we arrive at the same properties: If the numerator and denominator are the same then the fraction equals 1:         4                 =  1             4 If the denominator is 1 then the fraction is just the numerator         6                 =  6             1 If the numerator is 0 and the denominator is not 0, then the fraction equals 0         0                 =  0             9 If the denominator is zero then the fraction is undefined         2                   is  undefined            0 Applications Application of fractions are encountered everywhere.   Example    Use a fraction to describe each situation Out of ten problems on the test you scored nine correct Solution:   You got 9/10 of the problems right  Of the 75 patrons on Ellie's run, 61 were boarders Solution: The fraction of boarders on Ellie's run was 61/75 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 Of the seven students left in the class, three are women. Solution:  Seven days of January were snowy. Solution:  Fifteen of the ninety-one tourists are from Sacramento. Solution:      Back to the Fractions page Back to the Math 187A page Back to the Math Department page e-mail Questions and Suggestions