Estimating Fractions: We use estimation of fractions to check that the answer to a mixed number problem is correct. To estimate with fractions: 1. If the fraction part of a mixed number is less than \( \frac{1}{2} \), we round down. II. If the fraction part of a mixed number is greater than or equal to \( \frac{1}{2} \), we round up. 5. Round the number to estimate the answer. Estimate: a) \[ \begin{array}{r} 2 \frac{2}{5} \\ +13 \frac{4}{5} \\ \hline \end{array} \] Estimate: b) \( -1 \frac{7}{8} \) \[ +3 \frac{5}{8} \] 6. Perform the operation indicated. \( -\left|\frac{1}{2}-\frac{7}{4}\right|+1 \frac{3}{8} \)

To estimate \(2 \frac{2}{5} + 13 \frac{4}{5}\), we'll round the fractions first. Since \( \frac{2}{5} \) is less than \( \frac{1}{2} \), we round down to 0. Thus, \(2 \frac{2}{5}\) becomes 2. For \(13 \frac{4}{5}\), since \( \frac{4}{5} \) is greater than \( \frac{1}{2} \), we round up to 14. Adding these, we estimate \(2 + 14 = 16\). For the second estimation \( -1 \frac{7}{8} + 3 \frac{5}{8}\), round the fractions again. Here, \( \frac{7}{8} \) rounds up (to \( -1 \)), and \( \frac{5}{8} \) also rounds up (to 4). So, \( -1 + 4 = 3\) is the estimated answer. Let’s tackle the operation \( -\left|\frac{1}{2}-\frac{7}{4}\right|+ 1 \frac{3}{8}\). First, calculate \( \frac{1}{2} - \frac{7}{4} = \frac{2}{4} - \frac{7}{4} = -\frac{5}{4} \). Taking the absolute value gives us \( \left|-\frac{5}{4}\right| = \frac{5}{4} \). Insert that back into the equation: \( -\frac{5}{4} + 1 \frac{3}{8} \). Converting \( 1 \frac{3}{8} \) to an improper fraction gives us \( \frac{8}{8} + \frac{3}{8} = \frac{11}{8} \). The final operation is \( -\frac{5}{4} + \frac{11}{8}\). Noting that \( -\frac{5}{4} \) equals \( -\frac{10}{8} \), we arrive at \( -\frac{10}{8} + \frac{11}{8} = \frac{1}{8} \) as the final answer!