1. **Problem:** Arrange the fractions $\frac{2}{3}$, $1 \frac{5}{4}$, $\frac{5}{12}$, $\frac{9}{16}$ in descending order. 2. **Step 1:** Convert all mixed numbers to improper fractions. - $1 \frac{5}{4} = 1 + \frac{5}{4} = \frac{4}{4} + \frac{5}{4} = \frac{9}{4}$ 3. **Step 2:** Convert all fractions to decimals for easy comparison. - $\frac{2}{3} \approx 0.6667$ - $\frac{9}{4} = 2.25$ - $\frac{5}{12} \approx 0.4167$ - $\frac{9}{16} = 0.5625$ 4. **Step 3:** Arrange decimals in descending order: $2.25$, $0.6667$, $0.5625$, $0.4167$ 5. **Step 4:** Write the fractions back in order: $$\frac{9}{4} > \frac{2}{3} > \frac{9}{16} > \frac{5}{12}$$ **Final answer:** $\frac{9}{4}, \frac{2}{3}, \frac{9}{16}, \frac{5}{12}$