Applications

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Applied Problems Involving Fractions

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

Example

The width of a piece of paper is 8½ 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

$Diagram of a piece of paper that is 8.5 inches wide. 2/3 inches from left and right are shown and a rectangle with width x is inside that part.$

We see that the total width of 8½ 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 6½ dollars per hour at your job. For over time work you get 1½ 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          x              6 x 2 + 1 = 13
                       2            2             1         2           2

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

"I will earn $ 39 ."

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