#### Answer

3 pieces

#### Work Step by Step

Divide $6\frac{2}{3}$ by $1\frac{3}{4}$ to obtain:
$=6\frac{2}{3} \div 1\frac{3}{4}
\\=\frac{3(6)+2}{3} \div \frac{4(1)+3}{4}
\\=\frac{20}{3} \div \frac{7}{4}$
Use the rule $\frac{a}{b} \div \frac{c}{d} = \frac{[a}{b} \times \frac{d}{c}$ to obtain:
$\\=\frac{20}{3} \times \frac{4}{7}
\\=\frac{20(4)}{3(7)}
\\=\frac{80}{21}
\\=3\frac{17}{21}$
Thus, 3 pieces of pipes $1\frac{3}{4}$ ft long can be obtained from the original pipe.