Final answer:
After subtracting the length of the board cut and the saw cut from the original 33 1/4 inch board, the remaining length is 19 1/8 inches.
Step-by-step explanation:
To find out how much of the 33 1/4 inch board is left after cutting off a 13 3/4 inch piece and accounting for a 3/8 inch saw cut, we need to subtract the length of the piece removed and the width of the saw cut from the total length of the original board.
First, we convert all measurements to improper fractions to make it easier to subtract them:
- 33 1/4 inches = 133/4 inches = (4 * 33 + 1)/4 = 133/4 inches
- 13 3/4 inches = 55/4 inches = (4 * 13 + 3)/4 = 55/4 inches
- The saw cut = 3/8 inches
Now, we subtract both the length of the board cut and the saw cut from the total length of the original board:
- 133/4 - 55/4 - 3/8
- To subtract, we need a common denominator. The least common denominator for 4 and 8 is 8.
- So, we convert 133/4 to 266/8 and 55/4 to 110/8.
- Now, we subtract: 266/8 - 110/8 - 3/8 = 156/8 - 3/8 = 153/8 inches after simplifying
- Finally, we convert 153/8 back to a mixed number: 153/8 = 19 1/8 inches
Thus, the length of the original board left after the cut is 19 1/8 inches.