26. Выполните действия:

Решение:

1. \( \left( 1\frac{3}{5} + 1,8 \right) \cdot \frac{1}{2} = \left( \frac{8}{5} + \frac{18}{10} \right) \cdot \frac{1}{2} = \left( \frac{16}{10} + \frac{18}{10} \right) \cdot \frac{1}{2} = \frac{34}{10} \cdot \frac{1}{2} = \frac{17}{5} \cdot \frac{1}{2} = \frac{17}{10} = 1,7 \)
2. \( \left( 6 - 4\frac{8}{15} \right) : 2,2 = \left( 6 - \frac{68}{15} \right) : \frac{22}{10} = \left( \frac{90 - 68}{15} \right) : \frac{11}{5} = \frac{22}{15} : \frac{11}{5} = \frac{22}{15} \cdot \frac{5}{11} = \frac{2 \cdot 11}{3 \cdot 5} \cdot \frac{5}{11} = \frac{2}{3} \)
3. \( \left( 1,25 + \frac{1}{6} \right) \cdot 2,4 = \left( \frac{125}{100} + \frac{1}{6} \right) \cdot \frac{24}{10} = \left( \frac{5}{4} + \frac{1}{6} \right) \cdot \frac{12}{5} = \left( \frac{15 + 2}{12} \right) \cdot \frac{12}{5} = \frac{17}{12} \cdot \frac{12}{5} = \frac{17}{5} = 3,4 \)
4. \( 5,4 - 2\frac{1}{3} : 7\frac{2}{3} = \frac{54}{10} - \frac{7}{3} : \frac{23}{3} = \frac{27}{5} - \frac{7}{3} \cdot \frac{3}{23} = \frac{27}{5} - \frac{7}{23} = \frac{27 \cdot 23 - 7 \cdot 5}{5 \cdot 23} = \frac{621 - 35}{115} = \frac{586}{115} \)
5. \( 2\frac{1}{3} + 0,25 - 0,12 = \frac{7}{3} + \frac{25}{100} - \frac{12}{100} = \frac{7}{3} + \frac{1}{4} - \frac{3}{25} = \frac{7 \cdot 100 + 1 \cdot 75 - 3 \cdot 12}{300} = \frac{700 + 75 - 36}{300} = \frac{739}{300} \)
6. \( \left( 7,6 - 4\frac{3}{4} \right) : 1,9 = \left( \frac{76}{10} - \frac{19}{4} \right) : \frac{19}{10} = \left( \frac{38}{5} - \frac{19}{4} \right) : \frac{19}{10} = \left( \frac{152 - 95}{20} \right) : \frac{19}{10} = \frac{57}{20} : \frac{19}{10} = \frac{57}{20} \cdot \frac{10}{19} = \frac{3 \cdot 19}{2 \cdot 10} \cdot \frac{10}{19} = \frac{3}{2} = 1,5 \)

Ответ: 1) 1,7; 2) \( \frac{2}{3} \); 3) 3,4; 4) \( \frac{586}{115} \); 5) \( \frac{739}{300} \); 6) 1,5.