1. The problem is to divide the fractions $\frac{4}{7}$ by $\frac{1}{3}$.\n\n2. The formula for dividing fractions is:\n$$\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}$$\nThis means we multiply the first fraction by the reciprocal of the second fraction.\n\n3. Applying the formula:\n$$\frac{4}{7} \div \frac{1}{3} = \frac{4}{7} \times \frac{3}{1}$$\n\n4. Multiply the numerators and denominators:\n$$\frac{4 \times 3}{7 \times 1} = \frac{12}{7}$$\n\n5. Convert the improper fraction $\frac{12}{7}$ to a mixed number by dividing 12 by 7:\n$$12 \div 7 = 1 \text{ remainder } 5$$\nSo, the mixed number is:\n$$1 \frac{5}{7}$$\n\n6. The answer in simplest form as a mixed number is $1 \frac{5}{7}$.