d) \( 16 \frac{2}{3}: 7 \frac{1}{2} \)

To solve the expression \( 16 \frac{2}{3}: 7 \frac{1}{2} \), we will first convert the mixed numbers into improper fractions and then perform the division. 1. **Convert \( 16 \frac{2}{3} \) to an improper fraction:** \[ 16 \frac{2}{3} = 16 + \frac{2}{3} = \frac{16 \times 3 + 2}{3} = \frac{48 + 2}{3} = \frac{50}{3} \] 2. **Convert \( 7 \frac{1}{2} \) to an improper fraction:** \[ 7 \frac{1}{2} = 7 + \frac{1}{2} = \frac{7 \times 2 + 1}{2} = \frac{14 + 1}{2} = \frac{15}{2} \] 3. **Now, we can rewrite the division as a multiplication by the reciprocal:** \[ 16 \frac{2}{3} : 7 \frac{1}{2} = \frac{50}{3} \div \frac{15}{2} = \frac{50}{3} \times \frac{2}{15} \] 4. **Multiply the fractions:** \[ \frac{50 \times 2}{3 \times 15} = \frac{100}{45} \] 5. **Simplify the fraction:** \[ \frac{100}{45} = \frac{20}{9} \] Thus, the final answer is: \[ \frac{20}{9} \]