Convert mixed fractions to decimals: 15 3/4" = 15.75" and 31 1/4" = 31.25".
Calculate the total length used for the cut board and saw cut: 15.75" + 3/8" = 16 1/8".
Subtract the used length from the original board length: 31.25" - 16 1/8" = 15 1/2".
There are 15 1/2 inches remaining after cutting.
Convert mixed fractions to decimals: Since it's easier to work with decimals, let's first convert the mixed fractions to their decimal equivalents. 15 3/4 inches is equal to 15 + 3/4 = 15.75 inches. Similarly, 31 1/4 inches is equal to 31 + 1/4 = 31.25 inches.
Calculate the total length used for the cut board and saw cut: We know the cut board is 15.75 inches long, and the saw cut takes 3/8 of an inch (which is equal to 0.375 inches). Therefore, the total length used for the cut board and saw cut is 15.75 inches + 0.375 inches = 16.125 inches.
Subtract the used length from the original board length: Finally, we can find the remaining length of the original board by subtracting the total used length from its original length. This gives us 31.25 inches (original board) - 16.125 inches (used) = 15.125 inches.
Simplify the answer: To express the answer in a more readable format, we can convert the decimal back to a mixed fraction. Since 15.125 is equal to 15 + 1/8, the final answer is 15 1/2 inches.
Therefore, after cutting and accounting for the saw cut, 15 1/2 inches of the original 31 1/4 inch board remains.