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. \( -\left|\frac{1}{2}-\frac{7}{4}\right|+1 \frac{3}{8} \)

Let's estimate the mixed number problems step by step. ### Part a: Estimating \( 2 \frac{2}{5} + 13 \frac{4}{5} \) 1. **Identify the mixed numbers:** - \( 2 \frac{2}{5} \) - \( 13 \frac{4}{5} \) 2. **Estimate each mixed number:** - For \( 2 \frac{2}{5} \): - The fraction part \( \frac{2}{5} \) is less than \( \frac{1}{2} \), so we round down to \( 2 \). - For \( 13 \frac{4}{5} \): - The fraction part \( \frac{4}{5} \) is greater than \( \frac{1}{2} \), so we round up to \( 14 \). 3. **Add the estimated values:** \[ 2 + 14 = 16 \] ### Part b: Estimating \( -1 \frac{7}{8} + 3 \frac{5}{8} \) 1. **Identify the mixed numbers:** - \( -1 \frac{7}{8} \) - \( 3 \frac{5}{8} \) 2. **Estimate each mixed number:** - For \( -1 \frac{7}{8} \): - The fraction part \( \frac{7}{8} \) is greater than \( \frac{1}{2} \), so we round up to \( -1 \). - For \( 3 \frac{5}{8} \): - The fraction part \( \frac{5}{8} \) is also greater than \( \frac{1}{2} \), so we round up to \( 4 \). 3. **Add the estimated values:** \[ -1 + 4 = 3 \] ### Part c: Performing the operation \( -\left|\frac{1}{2}-\frac{7}{4}\right| + 1 \frac{3}{8} \) 1. **Calculate \( \frac{1}{2} - \frac{7}{4} \):** - Convert \( \frac{1}{2} \) to a fraction with a denominator of 4: \[ \frac{1}{2} = \frac{2}{4} \] - Now perform the subtraction: \[ \frac{2}{4} - \frac{7}{4} = \frac{2 - 7}{4} = \frac{-5}{4} \] 2. **Calculate the absolute value:** \[ \left| \frac{-5}{4} \right| = \frac{5}{4} \] 3. **Now perform the operation:** \[ -\left|\frac{1}{2}-\frac{7}{4}\right| + 1 \frac{3}{8} = -\frac{5}{4} + 1 \frac{3}{8} \] 4. **Convert \( 1 \frac{3}{8} \) to an improper fraction:** \[ 1 \frac{3}{8} = \frac{8}{8} + \frac{3}{8} = \frac{11}{8} \] 5. **Now perform the addition:** \[ -\frac{5}{4} + \frac{11}{8} \] - Convert \( -\frac{5}{4} \) to a fraction with a denominator of 8: \[ -\frac{5}{4} = -\frac{10}{8} \] - Now add: \[ -\frac{10}{8} + \frac{11}{8} = \frac{-10 + 11}{8} = \frac{1}{8} \] ### Summary of Estimates and Operations: - Part a estimate: \( 16 \) - Part b estimate: \( 3 \) - Part c result: \( \frac{1}{8} \)