Answer: Solve. a. \( 3 \frac{1}{4}-1 \frac{5}{6}= \) b. \( \frac{6}{7}-\frac{5}{9}= \)

**a. Solving \( 3 \frac{1}{4}-1 \frac{5}{6} \):** 1. Convert the mixed numbers to improper fractions: - \(3 \frac{1}{4} = \frac{3 \times 4 + 1}{4} = \frac{13}{4}\) - \(1 \frac{5}{6} = \frac{1 \times 6 + 5}{6} = \frac{11}{6}\) 2. Subtract the fractions by finding a common denominator: - The least common denominator of \(4\) and \(6\) is \(12\). - Write each fraction with denominator \(12\): - \(\frac{13}{4} = \frac{13 \times 3}{4 \times 3} = \frac{39}{12}\) - \(\frac{11}{6} = \frac{11 \times 2}{6 \times 2} = \frac{22}{12}\) 3. Perform the subtraction: \[ \frac{39}{12} - \frac{22}{12} = \frac{39 - 22}{12} = \frac{17}{12} \] 4. Convert the result to a mixed number: \[ \frac{17}{12} = 1 \frac{5}{12} \] **b. Solving \( \frac{6}{7}-\frac{5}{9} \):** 1. Find a common denominator for \(7\) and \(9\): - The least common denominator is \(63\). 2. Rewrite each fraction with the denominator \(63\): - \(\frac{6}{7} = \frac{6 \times 9}{7 \times 9} = \frac{54}{63}\) - \(\frac{5}{9} = \frac{5 \times 7}{9 \times 7} = \frac{35}{63}\) 3. Perform the subtraction: \[ \frac{54}{63} - \frac{35}{63} = \frac{54-35}{63} = \frac{19}{63} \] **Answers:** a. \( 1\frac{5}{12} \) b. \(\frac{19}{63}\)