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Lumber word question

Woodsmith magazine gave instructions on how to build a pine cupboard. Lumber will be needed for two shelves 11 1/4 inches long, two base sides 12 1/2 inches long, and two door stiles 28 1/8 inches long. Your lumber comes in 6 foot lengths.
a. How many feet of lumber will you need?
 
I've tried solving it 3 different times and I don't know what I'm doing wrong.

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Andy C. | Math/Physics TutorMath/Physics Tutor
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2 x (11 and 1/4) + 2 x (12 and 1/2) + 2 x (28 and 1/8) =
 
2 x 45/4  + 2 x 25/2 + 2 x 225/8 =
 
45/2 + 25 + 225/4 =
 
90/4 + 100/4 + 225/4 =
 
415/4 =
 
103 and 3/4 inches of lumber is needed
 
6 feet = 6 feet x 12 inches per foot = 72 inches
 
103 and 3/4 divided by 72 =
 
415/4 divided by 72 =
 
415 / 4 x 1/72  <--- remember when dividing fractions, KFC: keep, flip, change
 
415/ 288 =
 
1 and 127/288
 
Now,
288 = 2 x 144 = 2 x 12 x 12 = 2 x 2 x 2 x 3 x 2 x 2 x3.
So the only factors of 288 and 2 and 3, and neither one
divides 127 evenly. So the fraction is reduced to lowest terms.