1. **State the problem:** Find the quotient of $$\frac{1}{3} \div \frac{4}{9}$$ and simplify the answer completely. 2. **Recall the formula for dividing fractions:** To divide by a fraction, multiply by its reciprocal. $$\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}$$ 3. **Apply the formula:** $$\frac{1}{3} \div \frac{4}{9} = \frac{1}{3} \times \frac{9}{4}$$ 4. **Multiply the numerators and denominators:** $$= \frac{1 \times 9}{3 \times 4} = \frac{9}{12}$$ 5. **Simplify the fraction:** Find the greatest common divisor (GCD) of 9 and 12, which is 3. $$= \frac{\cancel{3} \times 3}{\cancel{3} \times 4} = \frac{3}{4}$$ 6. **Answer:** The quotient is $$\frac{3}{4}$$. Note: The problem states the quotient equals a negative value with a placeholder, but since both fractions are positive, the quotient is positive $$\frac{3}{4}$$. Therefore, the number that belongs in the green box is **3/4**.