1. The problem is to divide the fraction $\frac{4}{7}$ by $\frac{1}{3}$. 2. The formula for dividing fractions is: $$\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}$$ This means we multiply the first fraction by the reciprocal of the second fraction. 3. Applying the formula: $$\frac{4}{7} \div \frac{1}{3} = \frac{4}{7} \times \frac{3}{1}$$ 4. Multiply the numerators and denominators: $$\frac{4 \times 3}{7 \times 1} = \frac{12}{7}$$ 5. The fraction $\frac{12}{7}$ is an improper fraction and can be written as a mixed number: $$1 \frac{5}{7}$$ 6. Therefore, the final answer is $\frac{12}{7}$ or $1 \frac{5}{7}$.