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

To simplify the expression \( -5 \frac{1}{3} \div 4 \frac{1}{6} \times 1 \frac{7}{8} \), let's first convert the mixed numbers to improper fractions. 1. Convert \( -5 \frac{1}{3} \): \(-5 \frac{1}{3} = -\frac{16}{3}\) 2. Convert \( 4 \frac{1}{6} \): \(4 \frac{1}{6} = \frac{25}{6}\) 3. Convert \( 1 \frac{7}{8} \): \(1 \frac{7}{8} = \frac{15}{8}\) Now, we can rewrite the expression: \[ -\frac{16}{3} \div \frac{25}{6} \times \frac{15}{8} \] Next, we handle the division and multiplication in the correct order: \[ -\frac{16}{3} \div \frac{25}{6} = -\frac{16}{3} \times \frac{6}{25} = -\frac{16 \times 6}{3 \times 25} = -\frac{96}{75} \] To simplify \(-\frac{96}{75}\), we can find the greatest common divisor, which is \(3\): \[ -\frac{96 \div 3}{75 \div 3} = -\frac{32}{25} \] Finally, we multiply by \(\frac{15}{8}\): \[ -\frac{32}{25} \times \frac{15}{8} = -\frac{32 \times 15}{25 \times 8} = -\frac{480}{200} \] Simplifying \(-\frac{480}{200}\) gives us: \[ -\frac{480 \div 80}{200 \div 80} = -\frac{6}{2.5} = -\frac{12}{5} \] The final answer is: \[ -\frac{12}{5} \text{ or } -2 \frac{2}{5} \]