17. Найдите значение выражения: a) $$-\frac{12}{17} : \left(-1\frac{7}{17}\right) + 5,88 : (-14,7) - 0,1; б) \left(8-5\frac{3}{4}\right) \cdot 2\frac{2}{3} + \left(8-6\frac{3}{5}\right) : 1\frac{3}{4}; в) $$5,5-3\(\frac{3}{4}\) \(\cdot\) \(\left\)\(1\frac{2}{3}+1\frac{2}{5}\right\) : 2\(\frac{5}{9}\)$$; г) $$2\(\frac{4}{5}\) : 1\(\frac{2}{5}\) - 5\(\frac{1}{2}\) - 4\(\frac{2}{7}\) \(\cdot\) \(\frac{7}{15}\) \(\cdot\) \(\left\)\(1\frac{1}{2}\right\)^2$$; д) $$-\(\frac{5}{8}\) \(\cdot\) \(\frac{4}{15}\) - \(\frac{14}{33}\) : \(\left\)\(-\frac{7}{11}\right\) + \(\frac{1}{12}\)$$; e) $$\(\frac{2}{7}\) \(\cdot\) \(\left\)\(3\frac{1}{2}\right\)^2 - \(\frac{5}{13}\) : 3\(\frac{1}{13}\) + \(\frac{9}{10}\) : 3\(\frac{3}{5}\)$$.

Решение:

1. а) \( -\frac{12}{17} : \left(-1\frac{7}{17}\right) + 5.88 : (-14.7) - 0.1 \)



\( -1\frac{7}{17} = -\frac{17+7}{17} = -\frac{24}{17} \)


\( -\frac{12}{17} : (-\frac{24}{17}) = \frac{12}{17} \cdot \frac{17}{24} = \frac{12}{24} = \frac{1}{2} \)


\( 5.88 : (-14.7) = -0.4 \)


\( \frac{1}{2} - 0.4 - 0.1 = 0.5 - 0.4 - 0.1 = 0 \)


Ответ: 0

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



\( 8-5\frac{3}{4} = 7\frac{4}{4}-5\frac{3}{4} = 2\frac{1}{4} = \frac{9}{4} \)


\( 2\frac{2}{3} = \frac{8}{3} \)


\( \frac{9}{4} \cdot \frac{8}{3} = \frac{9 \cdot 8}{4 \cdot 3} = \frac{72}{12} = 6 \)


\( 8-6\frac{3}{5} = 7\frac{5}{5}-6\frac{3}{5} = 1\frac{2}{5} = \frac{7}{5} \)


\( 1\frac{3}{4} = \frac{7}{4} \)


\( \frac{7}{5} : \frac{7}{4} = \frac{7}{5} \cdot \frac{4}{7} = \frac{4}{5} \)


\( 6 + \frac{4}{5} = 6\frac{4}{5} \)


Ответ: $$6\frac{4}{5}$$

3. в) \( 5.5-3\frac{3}{4} \cdot \left(1\frac{2}{3}+1\frac{2}{5}\right) : 2\frac{5}{9} \)



\( 5.5 = \frac{11}{2} \)


\( 3\frac{3}{4} = \frac{15}{4} \)


\( 1\frac{2}{3} = \frac{5}{3} \)


\( 1\frac{2}{5} = \frac{7}{5} \)


\( \frac{5}{3} + \frac{7}{5} = \frac{25+21}{15} = \frac{46}{15} \)


\( 2\frac{5}{9} = \frac{23}{9} \)


\( \frac{15}{4} \cdot \frac{46}{15} = \frac{46}{4} = \frac{23}{2} \)


\( \frac{23}{2} : \frac{23}{9} = \frac{23}{2} \cdot \frac{9}{23} = \frac{9}{2} \)


\( \frac{11}{2} - \frac{9}{2} = \frac{2}{2} = 1 \)


Ответ: 1

4. г) \( 2\frac{4}{5} : 1\frac{2}{5} - 5\frac{1}{2} - 4\frac{2}{7} \cdot \frac{7}{15} \cdot \left(1\frac{1}{2}\right)^2 \)



\( 2\frac{4}{5} = \frac{14}{5} \)


\( 1\frac{2}{5} = \frac{7}{5} \)


\( \frac{14}{5} : \frac{7}{5} = \frac{14}{5} \cdot \frac{5}{7} = 2 \)


\( 5\frac{1}{2} = \frac{11}{2} \)


\( 4\frac{2}{7} = \frac{30}{7} \)


\( \left(1\frac{1}{2}\right)^2 = \left(\frac{3}{2}\right)^2 = \frac{9}{4} \)


\( \frac{30}{7} \cdot \frac{7}{15} \cdot \frac{9}{4} = \frac{30 \cdot 7 \cdot 9}{7 \cdot 15 \cdot 4} = \frac{2 \cdot 9}{4} = \frac{18}{4} = \frac{9}{2} \)


\( 2 - \frac{11}{2} - \frac{9}{2} = \frac{4}{2} - \frac{11}{2} - \frac{9}{2} = \frac{4-11-9}{2} = \frac{-16}{2} = -8 \)


Ответ: -8

5. д) \( -\frac{5}{8} \cdot \frac{4}{15} - \frac{14}{33} : \left(-\frac{7}{11}\right) + \frac{1}{12} \)



\( -\frac{5}{8} \cdot \frac{4}{15} = -\frac{5 \cdot 4}{8 \cdot 15} = -\frac{20}{120} = -\frac{1}{6} \)


\( -\frac{14}{33} : \left(-\frac{7}{11}\right) = \frac{14}{33} \cdot \frac{11}{7} = \frac{14 \cdot 11}{33 \cdot 7} = \frac{2 \cdot 1}{3 \cdot 1} = \frac{2}{3} \)


\( -\frac{1}{6} + \frac{2}{3} + \frac{1}{12} = -\frac{2}{12} + \frac{8}{12} + \frac{1}{12} = \frac{-2+8+1}{12} = \frac{7}{12} \)


Ответ: $$\frac{7}{12}$$

6. е) \( \frac{2}{7} \cdot \left(3\frac{1}{2}\right)^2 - \frac{5}{13} : 3\frac{1}{13} + \frac{9}{10} : 3\frac{3}{5} \)



\( 3\frac{1}{2} = \frac{7}{2} \)


\( \left(3\frac{1}{2}\right)^2 = \left(\frac{7}{2}\right)^2 = \frac{49}{4} \)


\( \frac{2}{7} \cdot \frac{49}{4} = \frac{2 \cdot 49}{7 \cdot 4} = \frac{1 \cdot 7}{1 \cdot 2} = \frac{7}{2} \)


\( 3\frac{1}{13} = \frac{40}{13} \)


\( \frac{5}{13} : \frac{40}{13} = \frac{5}{13} \cdot \frac{13}{40} = \frac{5}{40} = \frac{1}{8} \)


\( 3\frac{3}{5} = \frac{18}{5} \)


\( \frac{9}{10} : \frac{18}{5} = \frac{9}{10} \cdot \frac{5}{18} = \frac{9 \cdot 5}{10 \cdot 18} = \frac{1 \cdot 1}{2 \cdot 2} = \frac{1}{4} \)


\( \frac{7}{2} - \frac{1}{8} + \frac{1}{4} = \frac{28}{8} - \frac{1}{8} + \frac{2}{8} = \frac{28-1+2}{8} = \frac{29}{8} \)


Ответ: $$\frac{29}{8}$$