1.1 Выполните действия: 1) (1,8 + 1 2/7) : (1,8 - 1 2/7); 2) (1,5 + 1 1/3) : (7,6 - 5 1/3); 3) (23 - 15 1/3) : (-5 1/9); 4) (19 - 13 2/3) : (-7 1/9).

Краткое пояснение:

Пошаговое решение:

• 1.1.1:

  \[ \begin{array}{l} \left(1,8 + 1\frac{2}{7}\right) : \left(1,8 - 1\frac{2}{7}\right) = \left(\frac{18}{10} + \frac{9}{7}\right) : \left(\frac{18}{10} - \frac{9}{7}\right) \\ = \left(\frac{9}{5} + \frac{9}{7}\right) : \left(\frac{9}{5} - \frac{9}{7}\right) = \left(\frac{63+45}{35}\right) : \left(\frac{63-45}{35}\right) \\ = \frac{108}{35} : \frac{18}{35} = \frac{108}{35} \cdot \frac{35}{18} = \frac{108}{18} = 6 \end{array} \]

• 1.1.2:

  \[ \begin{array}{l} \left(1,5 + 1\frac{1}{3}\right) : \left(7,6 - 5\frac{1}{3}\right) = \left(\frac{15}{10} + \frac{4}{3}\right) : \left(\frac{76}{10} - \frac{16}{3}\right) \\ = \left(\frac{3}{2} + \frac{4}{3}\right) : \left(\frac{38}{5} - \frac{16}{3}\right) = \left(\frac{9+8}{6}\right) : \left(\frac{114-80}{15}\right) \\ = \frac{17}{6} : \frac{34}{15} = \frac{17}{6} \cdot \frac{15}{34} = \frac{1}{2} \cdot \frac{5}{2} = \frac{5}{4} = 1,25 \end{array} \]

• 1.1.3:

  \[ \begin{array}{l} \left(23 - 15\frac{1}{3}\right) : \left(-5\frac{1}{9}\right) = \left(\frac{69-15}{3}\right) : \left(-\frac{46}{9}\right) \\ = \frac{54}{3} : \left(-\frac{46}{9}\right) = 18 : \left(-\frac{46}{9}\right) \\ = 18 \cdot \left(-\frac{9}{46}\right) = -\frac{162}{46} = -\frac{81}{23} \end{array} \]

• 1.1.4:

  \[ \begin{array}{l} \left(19 - 13\frac{2}{3}\right) : \left(-7\frac{1}{9}\right) = \left(\frac{57-13}{3}\right) : \left(-\frac{64}{9}\right) \\ = \frac{44}{3} : \left(-\frac{64}{9}\right) = \frac{44}{3} \cdot \left(-\frac{9}{64}\right) \\ = \frac{11}{1} \cdot \left(-\frac{3}{16}\right) = -\frac{33}{16} \end{array} \]

Ответ: 1) 6; 2) 1,25; 3) -81/23; 4) -33/16