1. **State the problem:** We need to divide the mixed number $1 \frac{4}{5}$ by 2. 2. **Convert the mixed number to an improper fraction:** $$1 \frac{4}{5} = \frac{5 \times 1 + 4}{5} = \frac{9}{5}$$ 3. **Write the division as multiplication by the reciprocal:** $$\frac{9}{5} \div 2 = \frac{9}{5} \times \frac{1}{2}$$ 4. **Multiply the numerators and denominators:** $$\frac{9 \times 1}{5 \times 2} = \frac{9}{10}$$ 5. **Simplify the fraction if possible:** $\frac{9}{10}$ is already in simplest form. **Final answer:** $$\frac{9}{10}$$