1. **State the problem:** We need to find which of the given division expressions have the same quotient. 2. **Recall the division rule for fractions:** Dividing by a fraction is the same as multiplying by its reciprocal. That is, for any numbers $a$, $b$, and $c$ (with $b,c \neq 0$), $$a \div \frac{b}{c} = a \times \frac{c}{b}$$ 3. **Calculate each quotient:** - For $18 \div \frac{2}{3}$: $$18 \times \frac{3}{2} = \frac{18 \times 3}{2} = \frac{54}{2} = 27$$ - For $\frac{2}{3} \div \frac{1}{27}$: $$\frac{2}{3} \times \frac{27}{1} = \frac{2 \times 27}{3} = \frac{54}{3} = 18$$ - For $16 \div \frac{2}{5}$: $$16 \times \frac{5}{2} = \frac{16 \times 5}{2} = \frac{80}{2} = 40$$ - For $18 \div \frac{3}{2}$: $$18 \times \frac{2}{3} = \frac{18 \times 2}{3} = \frac{36}{3} = 12$$ - For $24 \div \frac{4}{3}$: $$24 \times \frac{3}{4} = \frac{24 \times 3}{4} = \frac{72}{4} = 18$$ 4. **Compare the quotients:** - $18 \div \frac{2}{3} = 27$ - $\frac{2}{3} \div \frac{1}{27} = 18$ - $16 \div \frac{2}{5} = 40$ - $18 \div \frac{3}{2} = 12$ - $24 \div \frac{4}{3} = 18$ 5. **Conclusion:** The expressions $\frac{2}{3} \div \frac{1}{27}$ and $24 \div \frac{4}{3}$ have the same quotient, which is 18.