avid and Patt each decomposed \( 1 \frac{3}{8} \). David wrote \( 1+\frac{1}{8}+\frac{3}{8} \). Patti wrote \( \frac{4}{8}+\frac{2}{8}+\frac{5}{8} \). Who is correct? Explain your reasoni Only David is correct. \( 1+\frac{1}{8}+\frac{3}{8}=1 \frac{3}{8} \), but \( \frac{4}{8}+\frac{2}{8}+\frac{5}{8}=\frac{11}{8} \) Ony Patti is correct \( \frac{4}{8}+\frac{2}{8}+\frac{5}{8}=1 \frac{3}{8} \), but \( 1+\frac{1}{8}+\frac{3}{8}=\frac{12}{8} \). Both Devid and Patti are correct. \( 1+\frac{1}{8}+\frac{3}{8}=1 \frac{3}{8} \), and \( \frac{4}{8}+\frac{2}{8}+\frac{5}{8}=1 \frac{3}{8} \). Neither David nor Pathi is correct. \( 1+\frac{1}{8}+\frac{3}{8}=\frac{12}{8} \), and \( \frac{4}{8}+\frac{2}{8}+\frac{5}{8}=\frac{11}{8} \).

Let's analyze the decompositions provided by David and Patti to determine who is correct. ### Original Fraction: \[ 1 \frac{3}{8} = \frac{11}{8} \] ### David's Decomposition: \[ 1 + \frac{1}{8} + \frac{3}{8} \] **Calculation:** \[ 1 + \frac{1}{8} + \frac{3}{8} = \frac{8}{8} + \frac{1}{8} + \frac{3}{8} = \frac{12}{8} = 1 \frac{1}{2} \] **Conclusion:** David's decomposition sums up to \(1 \frac{1}{2}\), which is \(\frac{12}{8}\). This does **not** equal the original fraction \(1 \frac{3}{8}\). ### Patti's Decomposition: \[ \frac{4}{8} + \frac{2}{8} + \frac{5}{8} \] **Calculation:** \[ \frac{4}{8} + \frac{2}{8} + \frac{5}{8} = \frac{11}{8} = 1 \frac{3}{8} \] **Conclusion:** Patti's decomposition accurately sums up to \(1 \frac{3}{8}\), which matches the original fraction. ### Summary of Options: 1. **Only David is correct.** - **Incorrect.** David's sum is \(1 \frac{1}{2}\), not \(1 \frac{3}{8}\). 2. **Only Patti is correct.** - **Correct.** Patti's sum correctly equals \(1 \frac{3}{8}\). 3. **Both David and Patti are correct.** - **Incorrect.** Only Patti's decomposition is accurate. 4. **Neither David nor Patti is correct.** - **Incorrect.** Patti's decomposition is correct. **Final Answer:** **Only Patti is correct.** \[ \frac{4}{8} + \frac{2}{8} + \frac{5}{8} = \frac{11}{8} = 1 \frac{3}{8} \] However, \[ 1 + \frac{1}{8} + \frac{3}{8} = \frac{12}{8} = 1 \frac{1}{2} \neq 1 \frac{3}{8} \]