Answer: Carpenter can cut 10 pieces.
Step-by-step explanation:
Given: The length of the board = [tex]18\frac{1}{2}\ feet=\frac{37}{2}\ feet[/tex]
Also, He needs to cut as many [tex]1\frac{3}{4}[/tex] feet long pieces as possible.
Then, the length of the pieces the carpenter can cut=[tex]\frac{37}{2}\div 1\frac{3}{4}[/tex]
[tex]\\=\frac{37}{2}\div \frac{7}{4}\\=\frac{37}{2}\times\frac{4}{7}\\=\frac{74}{7}\\= 10.57142\approx10[/tex]
Hence, the number of the pieces the carpenter can cut=10