1. Выполните действие: a) 4,6 ⋅ (−2,5); б) −25,344 : ; (−3,6); в) −1\frac{1}{7} ⋅ 1\frac{5}{16}; г) 1\frac{1}{8} : (−3\frac{3}{8}).

1. Выполните действие:

• a) 4,6 ⋅ (−2,5)
  • 4,6 ⋅ (−2,5) = −(4,6 ⋅ 2,5)
  • 4,6 ⋅ 2,5 = 46 ⋅ 0,25 = 46/4 = 23/2 = 11,5
  • Ответ: −11,5
• (−3,6) — это значение выражения из предыдущего пункта.
• б) −25,344 : — Недостаточно данных для решения.
• в) −1\frac{1}{7} ⋅ 1\frac{5}{16}
  • −1\frac{1}{7} = −\frac{7⋅1+1}{7} = −\frac{8}{7}
  • 1\frac{5}{16} = \frac{16⋅1+5}{16} = \frac{21}{16}
  • −\frac{8}{7} ⋅ \frac{21}{16} = −\frac{8⋅21}{7⋅16} = −\frac{168}{112}
  • Сокращаем дробь:
  • 168 = 2 ⋅ 84 = 2 ⋅ 2 ⋅ 42 = 2 ⋅ 2 ⋅ 2 ⋅ 21 = 2^3 ⋅ 3 ⋅ 7
  • 112 = 2 ⋅ 56 = 2 ⋅ 2 ⋅ 28 = 2 ⋅ 2 ⋅ 2 ⋅ 14 = 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 7 = 2^4 ⋅ 7
  • −\frac{2^3 ⋅ 3 ⋅ 7}{2^4 ⋅ 7} = −\frac{3}{2} = −1,5
  • Ответ: −1,5
• г) 1\frac{1}{8} : (−3\frac{3}{8})
  • 1\frac{1}{8} = \frac{8⋅1+1}{8} = \frac{9}{8}
  • −3\frac{3}{8} = −\frac{8⋅3+3}{8} = −\frac{27}{8}
  • \frac{9}{8} : (−\frac{27}{8}) = \frac{9}{8} ⋅ (−\frac{8}{27}) = −\frac{9⋅8}{8⋅27} = −\frac{9}{27} = −\frac{1}{3}
  • Ответ: −\frac{1}{3}