6.3
[tex]a) \ (\frac{2}{3}+\frac{1}{4}):1\frac{5}{6}+\frac{1}{2} = (\frac{8}{12}+\frac{3}{12}):\frac{11}{6}+\frac{1}{2} = \frac{11}{12}\cdot\frac{6}{11}+\frac{1}{2} = \frac{6}{12}+\frac{1}{2} = \frac{1}{2}+\frac{1}{2} = 1\\\\\\b) \ [(5\frac{1}{2}-3\frac{1}{4}):2\frac{1}{4}+7\frac{5}{8}]:2\frac{7}{8}=[(5\frac{2}{4}-3\frac{1}{4}):\frac{9}{4}+\frac{61}{8}]:\frac{23}{8} =(2\frac{1}{4}\cdot\frac{4}{9}+\frac{61}{8})\cdot\frac{8}{23}=[/tex]
[tex]=(\frac{9}{4}\cdot\frac{4}{9}+\frac{61}{8})\cdot\frac{8}{23}=(1+\frac{61}{8})\cdot\frac{8}{23} = \frac{69}{8}\cdot\frac{8}{23} = \frac{69}{23} = 3[/tex]
[tex]c) \ \frac{3}{4}-\frac{3}{2}+(2\frac{1}{2}-1\frac{7}{8}):\frac{1}{8}-2\frac{1}{4} = \frac{3}{4}+\frac{6}{4}+(\frac{5}{2}-\frac{15}{8})\cdot\frac{8}{1}-2\frac{1}{4}=\frac{9}{4}+(\frac{20}{8}-\frac{15}{8})\cdot8-2\frac{1}{4} =\\\\=\frac{9}{4}+\frac{5}{8}\cdot8-2\frac{1}{4} =2\frac{1}{4}+5-2\frac{1}{4} = 5[/tex]
[tex]d) \ (1\frac{1}{2}+2\frac{2}{3}):\frac{5}{6}-(3\frac{1}{3}-1\frac{1}{4}):2\frac{1}{12} =(\frac{3}{2}+\frac{8}{3})\cdot\frac{6}{5}-(\frac{10}{3}-\frac{5}{4}):\frac{25}{12}=\\\\=(\frac{9}{6}+\frac{16}{6})\cdot\frac{6}{5}-(\frac{40}{12}-\frac{15}{12})\cdot\frac{12}{25} = \frac{25}{6}\cdot\frac{6}{5}-\frac{25}{12}\cdot\frac{12}{25} = \frac{25}{5}-1 = 5-1 = 4[/tex]
