Roger wants to carpet a rectangular room with the length of 8 ¾ feet and a width of 9 1/3 feet. If he has 85 square feet of carpet, how many square feet of carpet will be left after he covers the floor of the room?

To find out how many square feet of carpet will be left, we need to first calculate the area of the room and then subtract it from the total area of the carpet.

Given:
Length of the room = 8 ¾ feet
Width of the room = 9 1/3 feet
Total area of the carpet = 85 square feet

To find the area of the room, multiply the length by the width:
Area of the room = (8 ¾ feet) * (9 1/3 feet)

To do this calculation, we need to convert the mixed numbers (8 ¾ and 9 1/3) to improper fractions:

8 ¾ = (8 * 4 + 1) / 4 = 33/4
9 1/3 = (9 * 3 + 1) / 3 = 28/3

Now, multiply the fractions to find the area:
Area of the room = (33/4) * (28/3)

To multiply fractions, multiply the numerators and multiply the denominators:
Area of the room = (33 * 28) / (4 * 3) = 924 / 12 = 77 square feet

Now, to find the remaining carpet, subtract the area of the room from the total area of the carpet:
Remaining carpet = Total area of carpet - Area of the room
Remaining carpet = 85 square feet - 77 square feet

Subtracting, we get:
Remaining carpet = 8 square feet

Therefore, after covering the floor of the room, Roger will have 8 square feet of carpet left.

8 3/4 = 35/4

9 1/3 = 28/3

35/4 * 28/3 = 980/12 = 245/3

85 = 255/3

so, 255/3 - 245/3 = 10/3