Final answer:
Alan will need to cut off 37/8 ft of the board to make the table.
Step-by-step explanation:
To find out how much of the board Alan will need to cut off, we subtract the length of the table from the length of the board. The table is 6 1/2 ft long and the board is 7 7/8 ft long. First, we convert the mixed numbers into improper fractions. The table is 6 1/2 ft = 13/2 ft, and the board is 7 7/8 ft = 63/8 ft. Next, we subtract: 63/8 ft - 13/2 ft = (63/8 ft) - (26/8 ft) = 37/8 ft.
Therefore, Alan will need to cut off 37/8 ft of the board to make the table.