1038. Выполните действия: 1) -2,7 - (-1,2) + 3,5 - (-2,8); 2)-7,4 - 0,6 - 3,8 - (-2,3); 3) (-9,3 - 1,7) - (2,6 + (-5,9)); 7 4) 4- (-1) -(-1)-(-): 12 11 15 45 64 81 13 19 5) - -6+(-1)-(-) 88 15 21 44711 6) (--). (5 -7-) 57912 1039 Hе выполняя вычислений сравните:

Решение:

1. 1) -2,7 - (-1,2) + 3,5 - (-2,8)

   Раскрываем скобки, помня, что минус на минус даёт плюс:

   -2,7 + 1,2 + 3,5 + 2,8

   Складываем числа:

   (-2,7 + 1,2) + (3,5 + 2,8) = -1,5 + 6,3 = 4,8

   Ответ: 4,8

2. 2) -7,4 - 0,6 - 3,8 ⋅ (-2,3)

   Сначала выполняем умножение:

   -3,8 ⋅ (-2,3) = 8,74

   Теперь выполняем вычитание и сложение:

   -7,4 - 0,6 + 8,74 = -8 + 8,74 = 0,74

   Ответ: 0,74

3. 3) (-9,3 - 1,7) ⋅ (2,6 + (-5,9))

   Выполняем действия в скобках:

   (-9,3 - 1,7) = -11

   (2,6 + (-5,9)) = -3,3

   Умножаем результаты:

   -11 ⋅ (-3,3) = 36,3

   Ответ: 36,3

4. 4) 4\(\frac{7}{12}\) ⋅ (-1\(\frac{3}{11}\)) - (-1\(\frac{1}{15}\)) ⋅ (-\(\frac{45}{64}\))

   Преобразуем смешанные числа в неправильные дроби:

   4\(\frac{7}{12}\) = \(\frac{55}{12}\)

   -1\(\frac{3}{11}\) = -\(\frac{14}{11}\)

   -1\(\frac{1}{15}\) = -\(\frac{16}{15}\)

   Выполняем умножение:

   \(\frac{55}{12}\) ⋅ (-\(\frac{14}{11}\)) = -\(\frac{55 ⋅ 14}{12 ⋅ 11}\) = -\(\frac{5 ⋅ 7}{6 ⋅ 1}\) = -\(\frac{35}{6}\)

   -\(\frac{16}{15}\) ⋅ (-\(\frac{45}{64}\)) = \(\frac{16 ⋅ 45}{15 ⋅ 64}\) = \(\frac{1 ⋅ 3}{1 ⋅ 4}\) = \(\frac{3}{4}\)

   Вычитаем:

   -\(\frac{35}{6}\) - \(\frac{3}{4}\) = -\(\frac{35 ⋅ 2}{6 ⋅ 2}\) - \(\frac{3 ⋅ 3}{4 ⋅ 3}\) = -\(\frac{70}{12}\) - \(\frac{9}{12}\) = -\(\frac{79}{12}\) = -6\(\frac{7}{12}\)

   Ответ: -6\(\frac{7}{12}\)

5. 5) -\(\frac{81}{88}\) ⋅ (-6 + (-1\(\frac{13}{15}\)) ⋅ (-1\(\frac{19}{21}\)))

   Преобразуем смешанные числа в неправильные дроби:

   -1\(\frac{13}{15}\) = -\(\frac{28}{15}\)

   -1\(\frac{19}{21}\) = -\(\frac{40}{21}\)

   Выполняем умножение в скобках:

   -\(\frac{28}{15}\) ⋅ (-\(\frac{40}{21}\)) = \(\frac{28 ⋅ 40}{15 ⋅ 21}\) = \(\frac{4 ⋅ 8}{3 ⋅ 3}\) = \(\frac{32}{9}\)

   Складываем числа в скобках:

   -6 + \(\frac{32}{9}\) = -\(\frac{6 ⋅ 9}{9}\) + \(\frac{32}{9}\) = -\(\frac{54}{9}\) + \(\frac{32}{9}\) = -\(\frac{22}{9}\)

   Умножаем:

   -\(\frac{81}{88}\) ⋅ (-\(\frac{22}{9}\)) = \(\frac{81 ⋅ 22}{88 ⋅ 9}\) = \(\frac{9 ⋅ 1}{4 ⋅ 1}\) = \(\frac{9}{4}\) = 2\(\frac{1}{4}\)

   Ответ: 2\(\frac{1}{4}\)

6. 6) (-\(\frac{4}{5}\) - \(\frac{4}{7}\)) ⋅ (5\(\frac{7}{9}\) - 7\(\frac{11}{12}\))

   Выполняем действия в скобках:

   -\(\frac{4}{5}\) - \(\frac{4}{7}\) = -\(\frac{4 ⋅ 7}{5 ⋅ 7}\) - \(\frac{4 ⋅ 5}{7 ⋅ 5}\) = -\(\frac{28}{35}\) - \(\frac{20}{35}\) = -\(\frac{48}{35}\)

   Преобразуем смешанные числа в неправильные дроби:

   5\(\frac{7}{9}\) = \(\frac{52}{9}\)

   7\(\frac{11}{12}\) = \(\frac{95}{12}\)

   Вычитаем:

   \(\frac{52}{9}\) - \(\frac{95}{12}\) = \(\frac{52 ⋅ 4}{9 ⋅ 4}\) - \(\frac{95 ⋅ 3}{12 ⋅ 3}\) = \(\frac{208}{36}\) - \(\frac{285}{36}\) = -\(\frac{77}{36}\)

   Умножаем результаты:

   -\(\frac{48}{35}\) ⋅ (-\(\frac{77}{36}\)) = \(\frac{48 ⋅ 77}{35 ⋅ 36}\) = \(\frac{4 ⋅ 11}{5 ⋅ 3}\) = \(\frac{44}{15}\) = 2\(\frac{14}{15}\)

   Ответ: 2\(\frac{14}{15}\)