Applied Problems Involving Fractions

We will follow the same method from 181A to solve applied problems that involve fractions.

Example

The width of a piece of paper is 8 inches.  If you want the left and right margins to be 2/3 inches, what is the width of the written part of the page?

Solution

We begin by stating our goal:

"The width of the written part of the page is          inches"

Next draw the picture letting x be the width of the written 

We see that the total width of 8 is made up of the two margins and the written space.  The margins take up

                 2            4
        2  x          =          
                 3            3

If we take away the margin width from the paper width, we get the width of the writing, that is

        

                    1         2
         x  = 8       -         
                    2         3

                 17         2
           =           -                
8 x 2 + 1 =  17
                   2         3

                 17 x 3         2 x 2
           =                 -                     
The LCD of 2 and 3 is 6
                   2 x 3         3 x 2

                 51         4              47               5
           =           -             =             =    7         
   6 x 7 + 5  =  47
                  6         
6               6                6

We can conclude that 

The width of the written part of the page is   7 5/6   inches.

 

Example

You earn 6 dollars per hour at your job.  For over time work you get 1 times your wages.  If you work 4 hour of overtime, how much overtime pay will you get?

Solution

We begin by writing our goal:

"I will earn $        ."

Because of the word "times" we see that this is a multiplication problem.  We write

        

                       1            1             4       13           3
           4 x  6         x  1           =                  x           
   6 x 2 + 1  =  13
                       2         
   2             1         2           2

               1       13           3          39
        =                  x           
                  We cancelled the 4 with the two 2's
            
   1         1           1           1

"I will earn $  39  ."

 



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