Multiple Choice Question Add Mlxed Numbers (Regroup) \[ \begin{array}{l}1 \frac{3}{4}+1 \frac{2}{4}=\text { ? } \\ \text { What is the sum wlthout an Improper fraction? } \\ \text { O } 2 \frac{5}{4}\end{array} \] \( \begin{array}{l}\text { O } 3 \frac{5}{4}\end{array} \)

To solve the problem of adding the mixed numbers \(1 \frac{3}{4}\) and \(1 \frac{2}{4}\), we will follow these steps: 1. **Convert the mixed numbers to improper fractions.** - For \(1 \frac{3}{4}\): \[ 1 \frac{3}{4} = \frac{1 \times 4 + 3}{4} = \frac{4 + 3}{4} = \frac{7}{4} \] - For \(1 \frac{2}{4}\): \[ 1 \frac{2}{4} = \frac{1 \times 4 + 2}{4} = \frac{4 + 2}{4} = \frac{6}{4} \] 2. **Add the improper fractions.** \[ \frac{7}{4} + \frac{6}{4} = \frac{7 + 6}{4} = \frac{13}{4} \] 3. **Convert the improper fraction back to a mixed number.** - To convert \(\frac{13}{4}\) to a mixed number, divide the numerator by the denominator: \[ 13 \div 4 = 3 \quad \text{(whole number part)} \] - The remainder is \(13 - (4 \times 3) = 1\). - Thus, \(\frac{13}{4} = 3 \frac{1}{4}\). 4. **Final answer:** The sum of \(1 \frac{3}{4} + 1 \frac{2}{4}\) is \(3 \frac{1}{4}\). Now, let's check the options provided: - \(2 \frac{5}{4}\) - \(3 \frac{5}{4}\) Since our calculated answer is \(3 \frac{1}{4}\), it does not match any of the options given. Therefore, the correct answer is \(3 \frac{1}{4}\), which is not listed among the options.