3. Fill in the missing numbers to form equivalent rates. \( \begin{array}{l}\text { a. } \frac{4 \mathrm{~L}}{10 \mathrm{~m}^{2}}=\frac{10 \mathrm{~L}}{5 \mathrm{~m}^{2}}=\frac{1}{\mathrm{~m}^{2}} \\ \text { b. } \frac{\$ 9}{6 \mathrm{~min}}=\frac{}{2 \mathrm{~min}}=\frac{}{10 \mathrm{~min}}=\frac{-}{1 \text { hour }}\end{array} \)

Sure, let's tackle both parts **a** and **b** of the problem by filling in the missing numbers to form equivalent rates. --- ### **3. Fill in the missing numbers to form equivalent rates.** #### **a.** Given: \[ \frac{4\, \text{L}}{10\, \text{m}^2} = \frac{10\, \text{L}}{5\, \text{m}^2} = \frac{1}{\text{m}^2} \] **Explanation:** All parts of the equation represent the rate in terms of liters per square meter (L/m²). Each fraction simplifies to the same rate: - \(\frac{4\, \text{L}}{10\, \text{m}^2} = \frac{2\, \text{L}}{5\, \text{m}^2}\) - \(\frac{10\, \text{L}}{5\, \text{m}^2} = \frac{2\, \text{L}}{1\, \text{m}^2}\) - \(\frac{1}{\text{m}^2}\) is the simplified unit rate. **Filled-In Equation:** \[ \frac{4\, \text{L}}{10\, \text{m}^2} = \frac{10\, \text{L}}{5\, \text{m}^2} = \frac{2\, \text{L}}{1\, \text{m}^2} \] --- #### **b.** Given: \[ \frac{\$9}{6\, \text{min}} = \frac{\underline{\hspace{1cm}}}{2\, \text{min}} = \frac{\underline{\hspace{1cm}}}{10\, \text{min}} = \frac{\underline{\hspace{1cm}}}{1\, \text{hour}} \] **Objective:** Fill in the blanks to represent equivalent rates in dollars for the given time intervals. **Step-by-Step Solution:** 1. **Determine the Unit Rate:** \[ \frac{\$9}{6\, \text{min}} = \frac{\$1.5}{1\, \text{min}} \] 2. **Calculate for 2 minutes:** \[ \$1.5 \times 2 = \$3 \] \[ \frac{\$3}{2\, \text{min}} \] 3. **Calculate for 10 minutes:** \[ \$1.5 \times 10 = \$15 \] \[ \frac{\$15}{10\, \text{min}} \] 4. **Calculate for 1 hour (60 minutes):** \[ \$1.5 \times 60 = \$90 \] \[ \frac{\$90}{1\, \text{hour}} \] **Filled-In Equation:** \[ \frac{\$9}{6\, \text{min}} = \frac{\$3}{2\, \text{min}} = \frac{\$15}{10\, \text{min}} = \frac{\$90}{1\, \text{hour}} \] --- ### **Final Answer:** **b.** \[ \frac{\$9}{6\, \text{min}} = \frac{\$3}{2\, \text{min}} = \frac{\$15}{10\, \text{min}} = \frac{\$90}{1\, \text{hour}} \] --- This ensures that all the rates are equivalent by maintaining the same ratio of dollars to time across different time intervals.