Final answer:
Keith must place the picture frame 7 feet from each side of the wall to center it. The width of the wall not occupied by the picture is 7 1/12 feet on each side after subtracting the picture width and dividing by 2.
Step-by-step explanation:
The question asks how far from each side of the wall a picture frame should be placed if the wall is 14 5/6 feet wide and the picture is 1 1/2 feet wide to ensure it is centered. To solve this, first, find the total width that the picture will not occupy by subtracting the width of the picture from the width of the wall: 14 5/6 feet - 1 1/2 feet. Then, convert the mixed numbers to improper fractions to make the subtraction easier: 89/6 feet - 3/2 feet. We can then find a common denominator and subtract, which gives us 85/6 feet. This is the total space on the wall not occupied by the picture. To find the space on each side, divide this result by 2, which yields 85/12 feet, or 7 1/12 feet. Finally, convert this back into a mixed number to make it 7 1/12 feet, which simplifies to 7 feet or option A.