1. **State the problem:** Divide $10 \frac{3}{5}$ by 2. 2. **Convert the mixed number to an improper fraction:** $$10 \frac{3}{5} = \frac{10 \times 5 + 3}{5} = \frac{50 + 3}{5} = \frac{53}{5}$$ 3. **Write the division as multiplication by the reciprocal:** $$\frac{53}{5} \div 2 = \frac{53}{5} \times \frac{1}{2}$$ 4. **Multiply the numerators and denominators:** $$\frac{53 \times 1}{5 \times 2} = \frac{53}{10}$$ 5. **Convert the improper fraction back to a mixed number:** Divide 53 by 10: $$53 \div 10 = 5 \text{ remainder } 3$$ So, $$\frac{53}{10} = 5 \frac{3}{10}$$ **Final answer:** $$10 \frac{3}{5} \div 2 = 5 \frac{3}{10}$$