1. **State the problem:** We have the list of numbers $\left| -\frac{5}{12} \right|$, $-\frac{4}{3}$, $0.5$, and $-4$. We want to find which two terms should be switched to arrange the list in ascending order. 2. **Calculate the values:** - $\left| -\frac{5}{12} \right| = \frac{5}{12} \approx 0.4167$ - $-\frac{4}{3} = -1.3333$ - $0.5$ is already decimal - $-4$ is already decimal 3. **Original list with decimals:** $[0.4167, -1.3333, 0.5, -4]$ 4. **Sort the list in ascending order:** $[-4, -1.3333, 0.4167, 0.5]$ 5. **Compare original and sorted lists:** - Original: $[0.4167, -1.3333, 0.5, -4]$ - Sorted: $[-4, -1.3333, 0.4167, 0.5]$ 6. **Identify which two terms to switch:** - The first term $0.4167$ and the last term $-4$ need to be switched to get the correct ascending order. **Final answer:** Switch $\left| -\frac{5}{12} \right|$ and $-4$ to arrange the list in ascending order.