1. The problem is to calculate the sum of the mixed numbers $1 \frac{4}{15}$ and $2 \frac{4}{5}$ and express the answer as a mixed number in simplest form. 2. First, convert the mixed numbers to improper fractions. $$1 \frac{4}{15} = \frac{1 \times 15 + 4}{15} = \frac{15 + 4}{15} = \frac{19}{15}$$ $$2 \frac{4}{5} = \frac{2 \times 5 + 4}{5} = \frac{10 + 4}{5} = \frac{14}{5}$$ 3. To add the fractions, find a common denominator. The denominators are 15 and 5. The least common denominator (LCD) is 15. 4. Convert $\frac{14}{5}$ to have denominator 15: $$\frac{14}{5} = \frac{14 \times 3}{5 \times 3} = \frac{42}{15}$$ 5. Now add the fractions: $$\frac{19}{15} + \frac{42}{15} = \frac{19 + 42}{15} = \frac{61}{15}$$ 6. Convert the improper fraction back to a mixed number by dividing numerator by denominator: $$61 \div 15 = 4 \text{ remainder } 1$$ So, $$\frac{61}{15} = 4 \frac{1}{15}$$ 7. The fraction $\frac{1}{15}$ is already in simplest form. Final answer: $$4 \frac{1}{15}$$