3. Выполните действия. a)-3 3/7 + (-2 1/4) ⋅ (-2/3)² б) (7 5/6 - 9 4/9 + 4 1/9) ⋅ (-1,3 - 7/10)

Ответ: a) -4 1/2; б) -3 3/10

1. а) -3 \(\frac{3}{7}\) + (-2 \(\frac{1}{4}\)) ⋅ (- \(\frac{2}{3}\))^2 = - \(\frac{24}{7}\) + (- \(\frac{9}{4}\)) ⋅ \(\frac{4}{9}\) = - \(\frac{24}{7}\) - \(\frac{9 \cdot 4}{4 \cdot 9}\) = - \(\frac{24}{7}\) - 1 = -3 \(\frac{3}{7}\) - 1 = -4 \(\frac{3}{7}\) = - \(\frac{31}{7}\)

2. Преобразуем смешанные числа в неправильные дроби: 7 \(\frac{5}{6}\) = \(\frac{47}{6}\); 9 \(\frac{4}{9}\) = \(\frac{85}{9}\); 4 \(\frac{1}{9}\) = \(\frac{37}{9}\); -1,3 = -\(\frac{13}{10}\)

3. Приведем дроби к общему знаменателю: \(\frac{47}{6}\) = \(\frac{47 \cdot 3}{6 \cdot 3}\) = \(\frac{141}{18}\); \(\frac{85}{9}\) = \(\frac{85 \cdot 2}{9 \cdot 2}\) = \(\frac{170}{18}\); \(\frac{37}{9}\) = \(\frac{37 \cdot 2}{9 \cdot 2}\) = \(\frac{74}{18}\)

4. б) (\(\frac{141}{18}\) - \(\frac{170}{18}\) + \(\frac{74}{18}\)) ⋅ (- \(\frac{13}{10}\) - \(\frac{7}{10}\)) = \(\frac{141 - 170 + 74}{18}\) ⋅ (-\(\frac{13 + 7}{10}\)) = \(\frac{45}{18}\) ⋅ (-\(\frac{20}{10}\)) = \(\frac{5}{2}\) ⋅ (-2) = -5

Ответ: a) -4 3/7; б) -5