\begin{tabular}{l} (1)) Which division expression represents Paige's speed in miles per minute? \\ \( \left.\left.\frac{1}{16} \div \frac{2}{3}\right] \frac{2}{3} \div 16\right] 16 \div \frac{2}{3}\left[\frac{2}{3} \div \frac{1}{16}\right. \) \\ \hline\end{tabular}

To determine Paige's speed in miles per minute, we need to set up the appropriate division expression based on the information provided. Speed is calculated as **distance divided by time**. Let's break down the options: 1. **Option A: \(\frac{1}{16} \div \frac{2}{3}\)** - **Interpretation:** This represents \(\frac{1}{16}\) miles divided by \(\frac{2}{3}\) minutes. - **Calculation:** \(\frac{1}{16} \div \frac{2}{3} = \frac{1}{16} \times \frac{3}{2} = \frac{3}{32}\) miles per minute. 2. **Option B: \(\frac{2}{3} \div 16\)** - **Interpretation:** This represents \(\frac{2}{3}\) miles divided by 16 minutes. - **Calculation:** \(\frac{2}{3} \div 16 = \frac{2}{3} \times \frac{1}{16} = \frac{2}{48} = \frac{1}{24}\) miles per minute. 3. **Option C: \(16 \div \frac{2}{3}\)** - **Interpretation:** This represents 16 miles divided by \(\frac{2}{3}\) minutes. - **Calculation:** \(16 \div \frac{2}{3} = 16 \times \frac{3}{2} = 24\) miles per minute. 4. **Option D: \(\frac{2}{3} \div \frac{1}{16}\)** - **Interpretation:** This represents \(\frac{2}{3}\) miles divided by \(\frac{1}{16}\) minutes. - **Calculation:** \(\frac{2}{3} \div \frac{1}{16} = \frac{2}{3} \times 16 = \frac{32}{3} \approx 10.\overline{6}\) miles per minute. **Conclusion:** Paige's speed should be represented as **distance divided by time**. Without additional context, if we assume that Paige travels \(\frac{1}{16}\) miles in \(\frac{2}{3}\) minutes, then the correct division expression is: \[ \boxed{\dfrac{\dfrac{1}{16}}{\dfrac{2}{3}}} \] This corresponds to **Option A**: \(\frac{1}{16} \div \frac{2}{3}\).