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

To solve the expression \( 2 \frac{1}{5} \times\left(\frac{4}{7}+\frac{2}{9}\right) \), first convert the mixed number to an improper fraction: \( 2 \frac{1}{5} = \frac{11}{5} \). Next, find a common denominator for \( \frac{4}{7} \) and \( \frac{2}{9} \). The least common multiple is 63; rewriting gives \( \frac{36}{63} + \frac{14}{63} = \frac{50}{63} \). Now multiply \( \frac{11}{5} \times \frac{50}{63} = \frac{550}{315} \); simplifying gives \( \frac{110}{63} \) or \( 1 \frac{47}{63} \). For the expression \( -\frac{4}{9}+1 \frac{3}{4} \div\left(-\frac{5}{8}\right) \), begin by converting \( 1 \frac{3}{4} \) to an improper fraction; it becomes \( \frac{7}{4} \). Dividing by \( -\frac{5}{8} \) is the same as multiplying by its reciprocal, so \( \frac{7}{4} \times -\frac{8}{5} = -\frac{56}{20} = -\frac{14}{5} \). Now adding \( -\frac{4}{9} \) to \( -\frac{14}{5} \) requires a common denominator. Converting to \( \frac{-36}{45} \) and \( -\frac{126}{45} \), thus combining gives \( -\frac{162}{45} \), simplifying yields \( -\frac{18}{5} \) or \( -3 \frac{3}{5} \).