1) \(\frac{3}{4} - \frac{1}{4} = \frac{3-1}{4} = \frac{2}{4} = \frac{1}{2}\)
2) \(1\frac{8}{15} + 2 = 3\frac{8}{15}\)
3) \(\frac{5}{9} + 1\frac{13}{27} = \frac{5}{9} + \frac{40}{27} = \frac{15}{27} + \frac{40}{27} = \frac{55}{27} = 2\frac{1}{27}\)
4) \(10\frac{1}{18} - 4\frac{2}{12} = 10\frac{1}{18} - 4\frac{1}{6} = 10\frac{1}{18} - 4\frac{3}{18} = 9\frac{19}{18} - 4\frac{3}{18} = 5\frac{16}{18} = 5\frac{8}{9}\)
5) \(2\frac{3}{8} \cdot \frac{3}{4} = \frac{19}{8} \cdot \frac{3}{4} = \frac{57}{32} = 1\frac{25}{32}\)
6) \(2\frac{1}{3} \cdot 1\frac{1}{5} = \frac{7}{3} \cdot \frac{6}{5} = \frac{42}{15} = \frac{14}{5} = 2\frac{4}{5}\)
7) \(\frac{4}{9} : \frac{8}{9} = \frac{4}{9} \cdot \frac{9}{8} = \frac{36}{72} = \frac{1}{2}\)
8) \(3\frac{1}{5} : 2\frac{2}{15} = \frac{16}{5} : \frac{32}{15} = \frac{16}{5} \cdot \frac{15}{32} = \frac{240}{160} = \frac{3}{2} = 1\frac{1}{2}\)