42. Вычислите:

Решение:

1. A) \( 3\frac{3}{7} - 4\frac{5}{6} = \frac{24}{7} - \frac{29}{6} = \frac{24 \cdot 6 - 29 \cdot 7}{42} = \frac{144 - 203}{42} = \frac{-59}{42} = -1\frac{17}{42} \)
2. Б) \( 2,3 - (-3,4) = 2,3 + 3,4 = 5,7 \)
3. B) \( 2,3 - 3,4 = -1,1 \)
4. Г) \( -4\frac{8}{15} - \left(-3\frac{7}{12}\right) = -4\frac{8}{15} + 3\frac{7}{12} = -\frac{68}{15} + \frac{43}{12} = \frac{-68 \cdot 4 + 43 \cdot 5}{60} = \frac{-272 + 215}{60} = \frac{-57}{60} = -\frac{19}{20} \)
5. Д) \( -4,5 - 5\frac{2}{3} = -4,5 - \frac{17}{3} = -\frac{9}{2} - \frac{17}{3} = \frac{-9 \cdot 3 - 17 \cdot 2}{6} = \frac{-27 - 34}{6} = \frac{-61}{6} = -10\frac{1}{6} \)
6. E) \( 3\frac{1}{3} \cdot \left(-1\frac{2}{7}\right) = \frac{10}{3} \cdot \left(-\frac{9}{7}\right) = -\frac{10 \cdot 9}{3 \cdot 7} = -\frac{10 \cdot 3}{7} = -\frac{30}{7} = -4\frac{2}{7} \)
7. Ë) \( \left(-1\frac{4}{5}\right) \cdot (-0,8) = -\frac{9}{5} \cdot \left(-\frac{4}{5}\right) = \frac{9 \cdot 4}{5 \cdot 5} = \frac{36}{25} = 1\frac{11}{25} \)
8. Ж) \( (-3,2) \cdot (-2,5) = 8 \)
9. 3) \( \left(-5\frac{5}{6}\right) \cdot \left(-3\frac{4}{7}\right) = \left(-\frac{35}{6}\right) \cdot \left(-\frac{25}{7}\right) = \frac{35 \cdot 25}{6 \cdot 7} = \frac{5 \cdot 25}{6} = \frac{125}{6} = 20\frac{5}{6} \)
10. И) \( (-4,5) \cdot 3,8 = -17,1 \)
11. Й) \( 3\frac{5}{6} - 5\frac{6}{7} = \frac{23}{6} - \frac{41}{7} = \frac{23 \cdot 7 - 41 \cdot 6}{42} = \frac{161 - 246}{42} = \frac{-85}{42} = -2\frac{1}{42} \)
12. K) \( 3,5 - (-5,7) = 3,5 + 5,7 = 9,2 \)
13. Л) \( -7\frac{8}{9} - \left(-3\frac{11}{12}\right) = -7\frac{8}{9} + 3\frac{11}{12} = -\frac{71}{9} + \frac{47}{12} = \frac{-71 \cdot 4 + 47 \cdot 3}{36} = \frac{-284 + 141}{36} = \frac{-143}{36} = -3\frac{35}{36} \)
14. M) \( -6\frac{1}{3} - 4,2 = -6\frac{1}{3} - 4\frac{1}{5} = -\frac{19}{3} - \frac{21}{5} = \frac{-19 \cdot 5 - 21 \cdot 3}{15} = \frac{-95 - 63}{15} = \frac{-158}{15} = -10\frac{8}{15} \)
15. H) \( 3,5 - 5,7 = -2,2 \)
16. O) \( 2\frac{2}{3} \cdot \left(-1\frac{1}{11}\right) = \frac{8}{3} \cdot \left(-\frac{12}{11}\right) = -\frac{8 \cdot 12}{3 \cdot 11} = -\frac{8 \cdot 4}{11} = -\frac{32}{11} = -2\frac{10}{11} \)
17. П) \( (-2,6) \cdot \left(-\frac{3}{5}\right) = \left(-\frac{26}{10}\right) \cdot \left(-\frac{3}{5}\right) = \left(-\frac{13}{5}\right) \cdot \left(-\frac{3}{5}\right) = \frac{13 \cdot 3}{5 \cdot 5} = \frac{39}{25} = 1\frac{14}{25} \)
18. P) \( (-4,8) \cdot (-3,5) = 16,8 \)
19. C) \( \left(-4\frac{2}{11}\right) \cdot \left(-1\frac{10}{23}\right) = \left(-\frac{46}{11}\right) \cdot \left(-\frac{33}{23}\right) = \frac{46 \cdot 33}{11 \cdot 23} = \frac{(2 \cdot 23) \cdot (3 \cdot 11)}{11 \cdot 23} = 2 \cdot 3 = 6 \)
20. T) \( (-3,5) \cdot 2,2 = -7,7 \)