1. **State the problem:** Evaluate the expression $$9.1 + (-3 \frac{4}{5})$$. 2. **Convert the mixed number to an improper fraction:** $$-3 \frac{4}{5} = -\left(3 + \frac{4}{5}\right) = -\frac{15}{5} - \frac{4}{5} = -\frac{19}{5}$$. 3. **Convert the decimal to a fraction:** $$9.1 = \frac{91}{10}$$. 4. **Find a common denominator to add the fractions:** The denominators are 10 and 5. The least common denominator (LCD) is 10. Convert $$-\frac{19}{5}$$ to denominator 10: $$-\frac{19}{5} = -\frac{19 \times 2}{5 \times 2} = -\frac{38}{10}$$. 5. **Add the fractions:** $$\frac{91}{10} + \left(-\frac{38}{10}\right) = \frac{91 - 38}{10} = \frac{53}{10}$$. 6. **Convert the result back to decimal:** $$\frac{53}{10} = 5.3$$. **Final answer:** $$9.1 + (-3 \frac{4}{5}) = 5.3$$.