1. **State the problem:** Divide the fraction $\frac{3}{4}$ by the mixed number $3 \frac{1}{3}$. Write the answer as a fraction or mixed number in simplest form. 2. **Convert the mixed number to an improper fraction:** $$3 \frac{1}{3} = \frac{3 \times 3 + 1}{3} = \frac{10}{3}$$ 3. **Write the division as multiplication by the reciprocal:** $$\frac{3}{4} \div \frac{10}{3} = \frac{3}{4} \times \frac{3}{10}$$ 4. **Multiply the numerators and denominators:** $$\frac{3 \times 3}{4 \times 10} = \frac{9}{40}$$ 5. **Simplify the fraction if possible:** The numerator 9 and denominator 40 have no common factors other than 1, so the fraction is already in simplest form. 6. **Final answer:** $$\boxed{\frac{9}{40}}$$