1. **State the problem:** We need to divide the mixed number $10 \frac{1}{3}$ by the mixed number $2 \frac{1}{15}$ and express the answer in simplest form. 2. **Convert mixed numbers to improper fractions:** - $10 \frac{1}{3} = \frac{10 \times 3 + 1}{3} = \frac{31}{3}$ - $2 \frac{1}{15} = \frac{2 \times 15 + 1}{15} = \frac{31}{15}$ 3. **Recall the division rule for fractions:** Dividing by a fraction is the same as multiplying by its reciprocal. 4. **Apply the division rule:** $$\frac{31}{3} \div \frac{31}{15} = \frac{31}{3} \times \frac{15}{31}$$ 5. **Simplify before multiplying:** - The $31$ in numerator and denominator cancels out. - So we have $$\frac{1}{3} \times 15 = \frac{15}{3}$$ 6. **Simplify the fraction:** $$\frac{15}{3} = 5$$ **Final answer:** $5$