1.
[tex]a) \ 5\dfrac{2}{3}+2\dfrac{3}{4} = 5\dfrac{8}{12}+2\dfrac{9}{12} =7\dfrac{17}{12} = 8\dfrac{5}{12}[/tex]
[tex]b) \ 6\dfrac{1}{2}-2\dfrac{7}{9} = 6\dfrac{9}{18}-2\dfrac{14}{18} = 5\dfrac{27}{18}-2\dfrac{14}{18} = 3\dfrac{13}{18}[/tex]
[tex]c) \ 1\dfrac{1}{5}\cdot2\dfrac{2}{9} = \dfrac{6}{5}\cdot\dfrac{20}{9} = \dfrac{6}{9}\cdot\dfrac{20}{5} = \dfrac{2}{3}\cdot4=\dfrac{8}{3} = 2\dfrac{2}{3}[/tex]
[tex]d) \ \dfrac{2}{5}:8 = \dfrac{2}{5}\cdot\dfrac{1}{8} = \dfrac{1}{5}\cdot\dfrac{1}{4} = \dfrac{1}{20}[/tex]
2.
[tex]a) \ 2\dfrac{1}{3}:14 = \dfrac{7}{3}\cdot\dfrac{1}{14} = \dfrac{1}{3}\cdot\dfrac{1}{2} =\dfrac{1}{6}[/tex]
[tex]b) \ 4\dfrac{7}{9}+3\dfrac{4}{9} = 7\dfrac{11}{9} = 8\dfrac{2}{9}[/tex]
[tex]c) \ 9\dfrac{1}{6}-7\dfrac{5}{6} = 8\dfrac{7}{6}-7\dfrac{5}{6} = 1\dfrac{2}{6} = 1\dfrac{1}{3}[/tex]
[tex]d) \ 3\dfrac{3}{4}:3\dfrac{1}{8} = \dfrac{15}{4}:\dfrac{25}{8} = \dfrac{15}{4}\cdot\dfrac{8}{25} = 3\cdot\dfrac{2}{5} = \dfrac{6}{5} = 1\dfrac{1}{5}[/tex]