П.17 Найдите значение выражения:

Решение:

а) \( \frac{12}{7} : \left(-\frac{1}{7}\right) + 5,88 : (-14,7) - 0,1 \)

1. \( \frac{12}{7} : \left(-\frac{1}{7}\right) = \frac{12}{7} · (-7) = -12 \)
2. \( 5,88 : (-14,7) = -0,4 \)
3. \( -12 + (-0,4) = -12,4 \)
4. \( -12,4 - 0,1 = -12,5 \)

б) \( \left(8-\frac{5}{4}\right) · \frac{2}{3} + \left(8-\frac{6}{5}\right) : \frac{1}{4} \)

1. \( 8 - \frac{5}{4} = \frac{32}{4} - \frac{5}{4} = \frac{27}{4} \)
2. \( \frac{27}{4} · \frac{2}{3} = \frac{9 · 1}{2 · 1} = \frac{9}{2} \)
3. \( 8 - \frac{6}{5} = \frac{40}{5} - \frac{6}{5} = \frac{34}{5} \)
4. \( \frac{34}{5} : \frac{1}{4} = \frac{34}{5} · 4 = \frac{136}{5} \)
5. \( \frac{9}{2} + \frac{136}{5} = \frac{45}{10} + \frac{272}{10} = \frac{317}{10} = 31,7 \)

в) \( 3 · \left(1\frac{2}{5} + 1\frac{2}{5}\right) : 2 \)

1. \( 1\frac{2}{5} + 1\frac{2}{5} = \frac{7}{5} + \frac{7}{5} = \frac{14}{5} \)
2. \( 3 · \frac{14}{5} = \frac{42}{5} \)
3. \( \frac{42}{5} : 2 = \frac{42}{5} · \frac{1}{2} = \frac{21}{5} = 4,2 \)

г) \( 2\frac{1}{5} : \frac{1}{5} - 4 \frac{1}{2} · \frac{2}{9} \)

1. \( 2\frac{1}{5} : \frac{1}{5} = \frac{11}{5} · 5 = 11 \)
2. \( 4\frac{1}{2} · \frac{2}{9} = \frac{9}{2} · \frac{2}{9} = 1 \)
3. \( 11 - 1 = 10 \)

д) \( -\frac{5}{8} · \frac{4}{15} - \frac{14}{33} : \frac{2}{3} \)

1. \( -\frac{5}{8} · \frac{4}{15} = -\frac{1}{2} · \frac{1}{3} = -\frac{1}{6} \)
2. \( \frac{14}{33} : \frac{2}{3} = \frac{14}{33} · \frac{3}{2} = \frac{7}{11} · 1 = \frac{7}{11} \)
3. \( -\frac{1}{6} - \frac{7}{11} = -\frac{11}{66} - \frac{42}{66} = -\frac{53}{66} \)

е) \( \frac{2}{7} · \left(3\frac{1}{2}\right)^2 - \frac{5}{13} \)

1. \( 3\frac{1}{2} = \frac{7}{2} \)
2. \( \left(\frac{7}{2}\right)^2 = \frac{49}{4} \)
3. \( \frac{2}{7} · \frac{49}{4} = \frac{1}{1} · \frac{7}{2} = \frac{7}{2} \)
4. \( \frac{7}{2} - \frac{5}{13} = \frac{91}{26} - \frac{10}{26} = \frac{81}{26} \)

Ответ: а) -12,5; б) 31,7; в) 4,2; г) 10; д) -\( \frac{53}{66} \); е) \( \frac{81}{26} \).