Final answer:
To find how many 10 3/4 inch pieces can be cut from a 75 1/4 inch board, convert mixed numbers to improper fractions and divide, yielding 7 full pieces.
Step-by-step explanation:
To determine how many pieces of wood that are 10 3/4 inches long can be cut from a board that is 75 1/4 inches long, we need to perform a division. First, we'll convert the mixed numbers to improper fractions to make the calculation easier. For the length of each piece:
- 10 3/4 inches = (10 × 4) + 3 = 40 + 3 = 43/4 inches
For the length of the board:
- 75 1/4 inches = (75 × 4) + 1 = 300 + 1 = 301/4 inches
Now, we divide the length of the board by the length of each piece:
- 301/4 ÷ 43/4 = 301/1 ÷ 4/43 = 301× 43/4× 1 = 301/1 ÷ 172/4 = 301/1 ÷ 43 = 7 pieces with a remainder
Jody can cut 7 pieces of wood that are 10 3/4 inches long from a 75 1/4 inch board. We ignore the remainder since Jody cannot cut a complete 10 3/4 inch piece from it. Therefore, the correct answer is B. 7.