Решение:
$\frac{0,8 : (\frac{4}{5} \cdot 1,25)}{0,64 - \frac{1}{25}} + \frac{(1,08 - \frac{2}{25}) : \frac{4}{7}}{(6\frac{5}{9} - 3\frac{1}{4}) \cdot 2\frac{2}{17}} + (1,2 \cdot 0,5) : \frac{4}{5} = 2\frac{1}{3}.$

$1) \frac{4}{5} \cdot 1,25 = \frac{4}{5} \cdot 1\frac{25}{100} = \frac{4}{5} \cdot 1\frac{1}{4} = \frac{4}{5} \cdot \frac{5}{4} = \frac{4 \cdot 5}{5 \cdot 4} = \frac{1 \cdot 1}{1 \cdot 1} = \frac{1}{1} = 1;$

$2) 0,8 : 1 = 0,8;$

$3) 0,64 - \frac{1}{25} = 0,64 - 0,04 = 0,6;$

$4) 0,8 : 0,6 = 8 : 6 = \frac{8}{6} = 1\frac{2}{6} = 1\frac{1}{3};$

$5) 1,08 - \frac{2}{25} = 1,08 - 0,08 = 1;$

$6) 1 : \frac{4}{7} = 1 \cdot \frac{7}{4} = \frac{7}{4} = 1\frac{3}{4};$

$7) 6\frac{5}{9} - 3\frac{1}{4} = 6 + \frac{20}{36} - 3 - \frac{9}{36} = 6 - 3 + \frac{20 - 9}{36} = 3 + \frac{11}{36} = 3\frac{11}{36};$

$8) 3\frac{11}{36} \cdot 2\frac{2}{17} = \frac{119}{36} \cdot \frac{36}{17} = \frac{119 \cdot 36}{36 \cdot 17} = \frac{7 \cdot 1}{1 \cdot 1} = \frac{7}{1} = 7;$

$9) 1\frac{3}{4} : 7 = \frac{7}{4} \cdot \frac{1}{7} = \frac{7 \cdot 1}{4 \cdot 7} = \frac{1 \cdot 1}{4 \cdot 1} = \frac{1}{4};$

$10) 1,2 \cdot 0,5 = 0,6;$

$11) 0,6 : \frac{4}{5} = \frac{6}{10} \cdot \frac{5}{4} = \frac{6 \cdot 5}{10 \cdot 4} = \frac{3 \cdot 1}{2 \cdot 2} = \frac{3}{4};$

$12) 1\frac{1}{3} + \frac{1}{4} = 1 + \frac{4}{12} + \frac{3}{12} = 1 + \frac{4 + 3}{12} = 1 + \frac{7}{12} = 1\frac{7}{12};$

$13) 1\frac{7}{12} + \frac{3}{4} = 1 + \frac{7}{12} + \frac{9}{12} = 1 + \frac{7 + 9}{12} = 1 + \frac{16}{12} = 1 + 1\frac{4}{12} = 2\frac{4}{12} = 2\frac{1}{3}.$
Ответ: $2\frac{1}{3}$.

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