A 15 1/2 foot board is cut into pieces 3 1/4 long for a bookcase. What is the length of the piece remaining after as many shelves as possible have been cut?

15.5 / 3.25 = 4.769 feet

0.769 * 12 = 9.228 inches

you cut four planks out of it

4*3.25 = 13 feet used
that leaves 2 1/2 feet

To find the length of the piece remaining after as many shelves as possible have been cut, we need to divide the length of the board by the length of each shelf and then find the remainder.

Step 1: Convert the length of the board and the length of each shelf into the same unit.
15 1/2 feet = (15 * 12) + 6 = 186 inches
3 1/4 feet = (3 * 12) + 1 = 37 inches

Step 2: Divide the length of the board by the length of each shelf.
186 inches ÷ 37 inches = 5 shelves (with no remainder)

Step 3: Calculate the length of the remaining piece.
Length of remaining piece = Length of board - (Number of shelves × Length of each shelf)
Length of remaining piece = 186 inches - (5 shelves × 37 inches)
Length of remaining piece = 186 inches - 185 inches
Length of remaining piece = 1 inch

Therefore, the length of the piece remaining after as many shelves as possible have been cut is 1 inch.

To find the length of the piece remaining after cutting, we need to determine how many shelves can be cut from the 15 1/2 foot board and then subtract the total length of those shelves from the original length.

First, let's convert the length of the board to a common fraction:
15 1/2 = (15*2 + 1)/2 = 31/2

Next, let's convert the length of each shelf to a common fraction:
3 1/4 = (3*4 + 1)/4 = 13/4

Now, we need to divide the length of the board by the length of each shelf to find the number of shelves that can be cut:
31/2 ÷ 13/4 = (31/2) × (4/13) = 31/2 × 4/13 = (31 × 4) / (2 × 13) = 124/26 = 62/13

Since we can only have a whole number of shelves, we can cut a maximum of 62 shelves from the board.

To find the total length of the shelves that can be cut, we multiply the length of each shelf by the number of shelves:
Total length of shelves = 62/13 × 13/4 = 62/4 = 31/2

Finally, subtracting the total length of the shelves from the original length of the board, we have:
Length remaining = 31/2 - 31/2 = 0

Therefore, the length of the piece remaining after as many shelves as possible have been cut is 0.