3. \( \frac{1}{3}+\frac{5}{6} \div \frac{5}{9} \) 4. \( -\frac{8}{9}+\frac{1}{9} \div\left(-\frac{1}{4}\right) \) 5. \( \frac{7}{8} \times\left(-\frac{7}{9}-\frac{1}{9}\right) \) 6. \( \frac{1}{3} \times\left(\frac{5}{8}+\frac{3}{4}\right) \) \( = \) \( = \) 7. \( \frac{4}{9}-\frac{2}{9} \div \frac{1}{3}+\left(-\frac{2}{3}\right) \) 8. \( \frac{3}{5}+\frac{7}{15} \div \frac{4}{5}-\left(-1 \frac{1}{5}\right) \)

Sure! Let's solve each of the given fraction problems step by step. --- ### **Problem 3** \[ \frac{1}{3} + \frac{5}{6} \div \frac{5}{9} \] **Step 1: Perform the Division** \[ \frac{5}{6} \div \frac{5}{9} = \frac{5}{6} \times \frac{9}{5} = \frac{45}{30} = \frac{3}{2} \] **Step 2: Add the Result to \(\frac{1}{3}\)** \[ \frac{1}{3} + \frac{3}{2} = \frac{2}{6} + \frac{9}{6} = \frac{11}{6} \text{ or } 1 \frac{5}{6} \] **Answer:** \(\frac{11}{6}\) or \(1 \frac{5}{6}\) --- ### **Problem 4** \[ -\frac{8}{9} + \frac{1}{9} \div \left(-\frac{1}{4}\right) \] **Step 1: Perform the Division** \[ \frac{1}{9} \div \left(-\frac{1}{4}\right) = \frac{1}{9} \times (-4) = -\frac{4}{9} \] **Step 2: Add the Results** \[ -\frac{8}{9} + \left(-\frac{4}{9}\right) = -\frac{12}{9} = -\frac{4}{3} \] **Answer:** \(-\frac{4}{3}\) --- ### **Problem 5** \[ \frac{7}{8} \times \left(-\frac{7}{9} - \frac{1}{9}\right) \] **Step 1: Simplify Inside the Parentheses** \[ -\frac{7}{9} - \frac{1}{9} = -\frac{8}{9} \] **Step 2: Multiply** \[ \frac{7}{8} \times \left(-\frac{8}{9}\right) = -\frac{56}{72} = -\frac{7}{9} \] **Answer:** \(-\frac{7}{9}\) --- ### **Problem 6** \[ \frac{1}{3} \times \left(\frac{5}{8} + \frac{3}{4}\right) \] **Step 1: Simplify Inside the Parentheses** Convert \(\frac{3}{4}\) to eighths: \[ \frac{3}{4} = \frac{6}{8} \] Add the fractions: \[ \frac{5}{8} + \frac{6}{8} = \frac{11}{8} \] **Step 2: Multiply** \[ \frac{1}{3} \times \frac{11}{8} = \frac{11}{24} \] **Answer:** \(\frac{11}{24}\) --- ### **Problem 7** \[ \frac{4}{9} - \frac{2}{9} \div \frac{1}{3} + \left(-\frac{2}{3}\right) \] **Step 1: Perform the Division** \[ \frac{2}{9} \div \frac{1}{3} = \frac{2}{9} \times 3 = \frac{6}{9} = \frac{2}{3} \] **Step 2: Substitute Back Into the Expression** \[ \frac{4}{9} - \frac{2}{3} + \left(-\frac{2}{3}\right) \] Convert all fractions to ninths: \[ \frac{4}{9} - \frac{6}{9} - \frac{6}{9} = \frac{4 - 6 - 6}{9} = \frac{-8}{9} \] **Answer:** \(-\frac{8}{9}\) --- ### **Problem 8** \[ \frac{3}{5} + \frac{7}{15} \div \frac{4}{5} - \left(-1 \frac{1}{5}\right) \] **Step 1: Perform the Division** \[ \frac{7}{15} \div \frac{4}{5} = \frac{7}{15} \times \frac{5}{4} = \frac{35}{60} = \frac{7}{12} \] **Step 2: Simplify the Negative Term** \[ -\left(-1 \frac{1}{5}\right) = +1 \frac{1}{5} = \frac{6}{5} \] **Step 3: Combine All Terms** \[ \frac{3}{5} + \frac{7}{12} + \frac{6}{5} \] Find a common denominator (60): \[ \frac{3}{5} = \frac{36}{60}, \quad \frac{7}{12} = \frac{35}{60}, \quad \frac{6}{5} = \frac{72}{60} \] Add them together: \[ \frac{36}{60} + \frac{35}{60} + \frac{72}{60} = \frac{143}{60} = 2 \frac{23}{60} \] **Answer:** \(\frac{143}{60}\) or \(2 \frac{23}{60}\) --- If you have any more problems or need further clarification, feel free to ask!