\(\frac{1\frac{7}{8} \times 2\frac{2}{5}}{6\frac{3}{4} \div \frac{3}{4}}\)

from numerator \(1 \frac{7}{8} \times 2 \frac{2}{5}\)

= \(\frac{15}{8} \times \frac{12}{5}\)

= \(\frac{3 \times 3}{2 \times 1} = \frac{9}{2}\)

from denominator \(6\frac{3}{4} \div \frac{3}{4}\)

= \(\frac{27}{4} \div \frac{3}{4}\)

= \(\frac{27}{4} \times \frac{4}{3}\)

= \(\frac{9 \times 1}{1 \times 1} = \frac{9}{1}\)

\(\frac{9}{2} \div \frac{9}{1} = \frac{9}{2} \times \frac{1}{9}\)

= \(\frac{1}{2}\)