42. Вычислите:

Решение:

1. \( 3\frac{3}{7} - 4\frac{5}{6} = \frac{24}{7} - \frac{29}{6} = \frac{24 \cdot 6 - 29 \cdot 7}{42} = \frac{144 - 203}{42} = -\frac{59}{42} = -1\frac{17}{42} \)
2. \( 2,3 - (-3,4) = 2,3 + 3,4 = 5,7 \)
3. \( 2,3 - 3,4 = -1,1 \)
4. \( -4\frac{8}{15} - ( -3\frac{7}{12} ) = -\frac{68}{15} + \frac{43}{12} = \frac{-68 \cdot 4 + 43 \cdot 5}{60} = \frac{-272 + 215}{60} = -\frac{57}{60} = -\frac{19}{20} = -0,95 \)
5. \( -4,5 - 5\frac{2}{3} = -4\frac{1}{2} - 5\frac{2}{3} = -\frac{9}{2} - \frac{17}{3} = \frac{-9 \cdot 3 - 17 \cdot 2}{6} = \frac{-27 - 34}{6} = -\frac{61}{6} = -10\frac{1}{6} \)
6. \( 3\frac{1}{3} \cdot (-1\frac{2}{7}) = \frac{10}{3} \cdot (-\frac{9}{7}) = -\frac{10 \cdot 3}{7} = -\frac{30}{7} = -4\frac{2}{7} \)
7. \( (-\frac{1}{5}) \cdot (-0,8) = \frac{1}{5} \cdot \frac{8}{10} = \frac{1}{5} \cdot \frac{4}{5} = \frac{4}{25} = 0,16 \)
8. \( (-3,2) \cdot (-2,5) = 8 \)
9. \( (-5\frac{5}{6}) \cdot (-3\frac{4}{7}) = (-\frac{35}{6}) \cdot (-\frac{25}{7}) = \frac{35 \cdot 25}{6 \cdot 7} = \frac{5 \cdot 25}{6} = \frac{125}{6} = 20\frac{5}{6} \)
10. \( (-4,5) \cdot 3,8 = -17,1 \)
11. \( 3\frac{5}{6} - 5\frac{5}{7} = \frac{23}{6} - \frac{40}{7} = \frac{23 \cdot 7 - 40 \cdot 6}{42} = \frac{161 - 240}{42} = -\frac{79}{42} = -1\frac{37}{42} \)
12. \( 3,5 - (-5,7) = 3,5 + 5,7 = 9,2 \)
13. \( -7\frac{8}{9} - ( -3\frac{11}{12} ) = -\frac{71}{9} + \frac{47}{12} = \frac{-71 \cdot 4 + 47 \cdot 3}{36} = \frac{-284 + 141}{36} = -\frac{143}{36} = -3\frac{35}{36} \)
14. \( -6\frac{1}{3} - 4,2 = -6\frac{1}{3} - 4\frac{1}{5} = -\frac{19}{3} - \frac{21}{5} = \frac{-19 \cdot 5 - 21 \cdot 3}{15} = \frac{-95 - 63}{15} = -\frac{158}{15} = -10\frac{8}{15} \)
15. \( 3,5 - 5,7 = -2,2 \)
16. \( 2\frac{2}{3} \cdot (-1\frac{1}{11}) = \frac{8}{3} \cdot (-\frac{12}{11}) = -\frac{8 \cdot 4}{11} = -\frac{32}{11} = -2\frac{10}{11} \)
17. \( (-2,6) \cdot (-\frac{3}{5}) = -2,6 \cdot (-0,6) = 1,56 \)
18. \( (-4,8) \cdot (-3,5) = 16,8 \)
19. \( (-\frac{4}{11}) \cdot (-1\frac{10}{23}) = (-\frac{4}{11}) \cdot (-\frac{33}{23}) = \frac{4}{11} \cdot \frac{33}{23} = \frac{4 \cdot 3}{23} = \frac{12}{23} \)
20. \( (-3,5) \cdot 2,2 = -7,7 \)

Ответ: A) -1\(\frac{17}{42}\); Б) 5,7; В) -1,1; Г) -0,95; Д) -10\(\frac{1}{6}\); E) -4\(\frac{2}{7}\); Ё) 0,16; Ж) 8; З) 20\(\frac{5}{6}\); И) -17,1; Й) -1\(\frac{37}{42}\); К) 9,2; Л) -3\(\frac{35}{36}\); M) -10\(\frac{8}{15}\); H) -2,2; O) -2\(\frac{10}{11}\); П) 1,56; Р) 16,8; C) \(\frac{12}{23}\); Т) -7,7.