9.Найти значение выражений:

Решение:

а) \( (-15,64 : \frac{4}{5} + 7,1) \cdot \frac{2}{7} \)

1. \( -15,64 : \frac{4}{5} = -15.64 \cdot \frac{5}{4} = -3.91 \cdot 5 = -19.55 \)
2. \( -19.55 + 7.1 = -12.45 \)
3. \( -12.45 \cdot \frac{2}{7} = -\frac{1245}{100} \cdot \frac{2}{7} = -\frac{1245}{50} \cdot \frac{1}{7} = -\frac{177.857}{7} \approx -25.4 \)

б) \( (0,4 - \frac{11}{15}) : (\frac{1}{2} - \frac{7}{18} - (0,5) : \frac{1}{6}) \)

1. \( 0.4 - \frac{11}{15} = \frac{4}{10} - \frac{11}{15} = \frac{2}{5} - \frac{11}{15} = \frac{6-11}{15} = -\frac{5}{15} = -\frac{1}{3} \)
2. \( 0.5 : \frac{1}{6} = \frac{1}{2} : \frac{1}{6} = \frac{1}{2} \cdot 6 = 3 \)
3. \( \frac{1}{2} - \frac{7}{18} - 3 = \frac{9 - 7}{18} - 3 = \frac{2}{18} - 3 = \frac{1}{9} - 3 = \frac{1 - 27}{9} = -\frac{26}{9} \)
4. \( -\frac{1}{3} : -\frac{26}{9} = -\frac{1}{3} \cdot -\frac{9}{26} = \frac{9}{3 \cdot 26} = \frac{3}{26} \)

в) \( 0,8 : ((\frac{2}{3}) + \frac{5}{9}) \)

1. \( \frac{2}{3} + \frac{5}{9} = \frac{6+5}{9} = \frac{11}{9} \)
2. \( 0.8 : \frac{11}{9} = \frac{8}{10} : \frac{11}{9} = \frac{4}{5} \cdot \frac{9}{11} = \frac{36}{55} \)

г) \( 37,12-5,6:0,14 \)

1. \( 5.6 : 0.14 = \frac{56}{10} : \frac{14}{100} = \frac{56}{10} \cdot \frac{100}{14} = 4 \cdot 10 = 40 \)
2. \( 37.12 - 40 = -2.88 \)

д) \( 1,21+3,4-0,35 \)

1. \( 1.21 + 3.4 = 4.61 \)
2. \( 4.61 - 0.35 = 4.26 \)

е) \( (2,17 \cdot 3,7 - 1,83 \cdot 2,3) : 19,1 \)

1. \( 2.17 \cdot 3.7 = 7.989 \)
2. \( 1.83 \cdot 2.3 = 4.209 \)
3. \( 7.989 - 4.209 = 3.78 \)
4. \( 3.78 : 19.1 = \frac{378}{100} : \frac{191}{10} = \frac{378}{100} \cdot \frac{10}{191} = \frac{378}{10 \cdot 191} = \frac{378}{1910} \approx 0.1979 \)

ё) \( \frac{4}{19} \cdot 5 \frac{3}{7} + 1 \frac{15}{19} : \frac{7}{25} - 1 \frac{2}{3} \)

1. \( 5 \frac{3}{7} = \frac{38}{7} \)
2. \( 1 \frac{15}{19} = \frac{34}{19} \)
3. \( \frac{4}{19} \cdot \frac{38}{7} = \frac{4 \cdot 2}{7} = \frac{8}{7} \)
4. \( \frac{34}{19} : \frac{7}{25} = \frac{34}{19} \cdot \frac{25}{7} = \frac{850}{133} \)
5. \( \frac{8}{7} + \frac{850}{133} - \frac{2}{3} = \frac{8 \cdot 19}{133} + \frac{850}{133} - \frac{2}{3} = \frac{152+850}{133} - \frac{2}{3} = \frac{1002}{133} - \frac{2}{3} \)
6. \( \frac{1002 \cdot 3 - 2 \cdot 133}{133 \cdot 3} = \frac{3006 - 266}{399} = \frac{2740}{399} \approx 6.867 \)

ж) \( (\frac{1}{3} - 2 \frac{2}{3}) \cdot 2,4 \)

1. \( \frac{1}{3} - 2 \frac{2}{3} = \frac{1}{3} - \frac{8}{3} = -\frac{7}{3} \)
2. \( -\frac{7}{3} \cdot 2.4 = -\frac{7}{3} \cdot \frac{24}{10} = -\frac{7 \cdot 8}{10} = -\frac{56}{10} = -5.6 \)

з) \( (15,5 + 4,5) : 2 \frac{1}{2} \cdot 5 \frac{7}{12} - (2 \frac{1}{2} + 1 \frac{1}{3}) : 1 \frac{1}{6} \)

1. \( 15.5 + 4.5 = 20 \)
2. \( 2 \frac{1}{2} = \frac{5}{2} \)
3. \( 5 \frac{7}{12} = \frac{67}{12} \)
4. \( 20 : \frac{5}{2} = 20 \cdot \frac{2}{5} = 8 \)
5. \( 8 \cdot \frac{67}{12} = \frac{2 \cdot 67}{3} = \frac{134}{3} \)
6. \( 2 \frac{1}{2} = \frac{5}{2} \)
7. \( 1 \frac{1}{3} = \frac{4}{3} \)
8. \( \frac{5}{2} + \frac{4}{3} = \frac{15+8}{6} = \frac{23}{6} \)
9. \( 1 \frac{1}{6} = \frac{7}{6} \)
10. \( \frac{23}{6} : \frac{7}{6} = \frac{23}{6} \cdot \frac{6}{7} = \frac{23}{7} \)
11. \( \frac{134}{3} - \frac{23}{7} = \frac{134 \cdot 7 - 23 \cdot 3}{21} = \frac{938 - 69}{21} = \frac{869}{21} \approx 41.38 \)

и) \( (2 \frac{7}{15} + 1 \frac{7}{12}) \cdot 1 \frac{1}{9} - 1 \frac{7}{8} \)

1. \( 2 \frac{7}{15} = \frac{37}{15} \)
2. \( 1 \frac{7}{12} = \frac{19}{12} \)
3. \( 1 \frac{1}{9} = \frac{10}{9} \)
4. \( 1 \frac{7}{8} = \frac{15}{8} \)
5. \( \frac{37}{15} + \frac{19}{12} = \frac{37 \cdot 4 + 19 \cdot 5}{60} = \frac{148+95}{60} = \frac{243}{60} = \frac{81}{20} \)
6. \( \frac{81}{20} \cdot \frac{10}{9} = \frac{81 \cdot 1}{2 \cdot 9} = \frac{9 \cdot 1}{2 \cdot 1} = \frac{9}{2} \)
7. \( \frac{9}{2} - \frac{15}{8} = \frac{9 \cdot 4 - 15}{8} = \frac{36-15}{8} = \frac{21}{8} \)

к) \( (6 \frac{1}{7} - 5 \frac{3}{4}) : \frac{11}{14} + (3 \frac{3}{4} - 1 \frac{5}{6}) : 1 \frac{1}{6} \)

1. \( 6 \frac{1}{7} = \frac{43}{7} \)
2. \( 5 \frac{3}{4} = \frac{23}{4} \)
3. \( 3 \frac{3}{4} = \frac{15}{4} \)
4. \( 1 \frac{5}{6} = \frac{11}{6} \)
5. \( 1 \frac{1}{6} = \frac{7}{6} \)
6. \( \frac{43}{7} - \frac{23}{4} = \frac{43 \cdot 4 - 23 \cdot 7}{28} = \frac{172 - 161}{28} = \frac{11}{28} \)
7. \( \frac{11}{28} : \frac{11}{14} = \frac{11}{28} \cdot \frac{14}{11} = \frac{14}{28} = \frac{1}{2} \)
8. \( \frac{15}{4} - \frac{11}{6} = \frac{15 \cdot 3 - 11 \cdot 2}{12} = \frac{45 - 22}{12} = \frac{23}{12} \)
9. \( \frac{23}{12} : \frac{7}{6} = \frac{23}{12} \cdot \frac{6}{7} = \frac{23}{2 \cdot 7} = \frac{23}{14} \)
10. \( \frac{1}{2} + \frac{23}{14} = \frac{7 + 23}{14} = \frac{30}{14} = \frac{15}{7} \)

Ответ: а) -25.4; б) \( \frac{3}{26} \); в) \( \frac{36}{55} \); г) -2.88; д) 4.26; е) \( \frac{2740}{399} \); ё) \( \frac{869}{21} \); ж) -5.6; з) \( \frac{869}{21} \); и) \( \frac{21}{8} \); к) \( \frac{15}{7} \).