1. **State the problem:** We need to calculate $3 \div \frac{17}{5}$ and simplify the result. 2. **Recall the division rule for fractions:** Dividing by a fraction is the same as multiplying by its reciprocal. So, $$3 \div \frac{17}{5} = 3 \times \frac{5}{17}$$ 3. **Perform the multiplication:** $$3 \times \frac{5}{17} = \frac{3 \times 5}{17} = \frac{15}{17}$$ 4. **Simplify the fraction:** The numerator 15 and denominator 17 have no common factors other than 1, so the fraction is already in simplest form. **Final answer:** $$\frac{15}{17}$$