1. **State the problem:** Calculate $3 \frac{3}{10} - 1 \frac{4}{5}$. 2. **Convert mixed numbers to improper fractions:** $3 \frac{3}{10} = \frac{3 \times 10 + 3}{10} = \frac{33}{10}$ $1 \frac{4}{5} = \frac{1 \times 5 + 4}{5} = \frac{9}{5}$ 3. **Find common denominator:** Denominators are 10 and 5. Least common denominator is 10. 4. **Convert fractions to have common denominator:** $\frac{33}{10}$ remains $\frac{33}{10}$ $\frac{9}{5} = \frac{9 \times 2}{5 \times 2} = \frac{18}{10}$ 5. **Subtract the fractions:** $\frac{33}{10} - \frac{18}{10} = \frac{33 - 18}{10} = \frac{15}{10}$ 6. **Simplify the result:** $\frac{15}{10} = \frac{3 \times 5}{2 \times 5} = \frac{3}{2} = 1 \frac{1}{2}$ **Final answer:** $1 \frac{1}{2}$.