Контрольные задания > 5.9. Упростите выражение: A) 2/3 a ⋅ (-6b) ⋅ (-1/8) Б) -1 1/2 b ⋅ (-0.5) ⋅ (-4c) В) 3/8 m ⋅ (-2/3 n) ⋅ 7/8 Г) -m ⋅ (-n) Д) -a ⋅ (-b) ⋅ (-c) ⋅ (-d) Е) -3a ⋅ (-2b) ⋅ 3c ⋅ (-4) Ё) -5a ⋅ 6b ⋅ (-0,3c) Ж) -1/2 m ⋅ 0,3n ⋅ (-5p) ⋅ (-1 1/3) З) 3ab ⋅ 2 И) -mn ⋅ (-5) Й) 3xy ⋅ 4z К) -6ab ⋅ (-4bc) Л) 3/4 a ⋅ 1/3 c М) -2/3 m ⋅ 3/8 n Н) 4/5 a ⋅ (-3/8 b) ⋅ 5/9 c О) 3/7 m ⋅ 7/9 n ⋅ 6k П) -6a ⋅ 0,7b ⋅ (-0,5c)
Вопрос:

5.9. Упростите выражение: A) 2/3 a ⋅ (-6b) ⋅ (-1/8) Б) -1 1/2 b ⋅ (-0.5) ⋅ (-4c) В) 3/8 m ⋅ (-2/3 n) ⋅ 7/8 Г) -m ⋅ (-n) Д) -a ⋅ (-b) ⋅ (-c) ⋅ (-d) Е) -3a ⋅ (-2b) ⋅ 3c ⋅ (-4) Ё) -5a ⋅ 6b ⋅ (-0,3c) Ж) -1/2 m ⋅ 0,3n ⋅ (-5p) ⋅ (-1 1/3) З) 3ab ⋅ 2 И) -mn ⋅ (-5) Й) 3xy ⋅ 4z К) -6ab ⋅ (-4bc) Л) 3/4 a ⋅ 1/3 c М) -2/3 m ⋅ 3/8 n Н) 4/5 a ⋅ (-3/8 b) ⋅ 5/9 c О) 3/7 m ⋅ 7/9 n ⋅ 6k П) -6a ⋅ 0,7b ⋅ (-0,5c)

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Ответ:

Краткое пояснение: Упростим каждое выражение, перемножая числовые коэффициенты и переменные.
  1. А) \[\frac{2}{3} a \cdot (-6b) \cdot \left(-\frac{1}{8}\right) = \frac{2}{3} \cdot (-6) \cdot \left(-\frac{1}{8}\right) \cdot a \cdot b = \frac{12}{24} ab = \frac{1}{2} ab\]
  2. Б) \[-1\frac{1}{2} b \cdot (-0.5) \cdot (-4c) = -\frac{3}{2} b \cdot (-0.5) \cdot (-4c) = -\frac{3}{2} \cdot (-0.5) \cdot (-4) bc = -3bc\]
  3. В) \[\frac{3}{8} m \cdot \left(-\frac{2}{3} n\right) \cdot \frac{7}{8} = \frac{3}{8} \cdot \left(-\frac{2}{3}\right) \cdot \frac{7}{8} mn = -\frac{42}{192} mn = -\frac{7}{32} mn\]
  4. Г) \[-m \cdot (-n) = mn\]
  5. Д) \[-a \cdot (-b) \cdot (-c) \cdot (-d) = abcd\]
  6. Е) \[-3a \cdot (-2b) \cdot 3c \cdot (-4) = -3 \cdot (-2) \cdot 3 \cdot (-4) abc = -72abc\]
  7. Ё) \[-5a \cdot 6b \cdot (-0.3c) = -5 \cdot 6 \cdot (-0.3) abc = 9abc\]
  8. Ж) \[-\frac{1}{2} m \cdot 0.3n \cdot (-5p) \cdot \left(-1\frac{1}{3}\right) = -\frac{1}{2} \cdot 0.3 \cdot (-5) \cdot \left(-\frac{4}{3}\right) mnp = -\frac{6}{6} mnp = -mnp\]
  9. З) \[3ab \cdot 2 = 6ab\]
  10. И) \[-mn \cdot (-5) = 5mn\]
  11. Й) \[3xy \cdot 4z = 12xyz\]
  12. К) \[-6ab \cdot (-4bc) = -6 \cdot (-4) abbc = 24ab^2c\]
  13. Л) \[\frac{3}{4} a \cdot \frac{1}{3} c = \frac{3}{4} \cdot \frac{1}{3} ac = \frac{1}{4} ac\]
  14. М) \[-\frac{2}{3} m \cdot \frac{3}{8} n = -\frac{2}{3} \cdot \frac{3}{8} mn = -\frac{6}{24} mn = -\frac{1}{4} mn\]
  15. Н) \[\frac{4}{5} a \cdot \left(-\frac{3}{8} b\right) \cdot \frac{5}{9} c = \frac{4}{5} \cdot \left(-\frac{3}{8}\right) \cdot \frac{5}{9} abc = -\frac{60}{360} abc = -\frac{1}{6} abc\]
  16. О) \[\frac{3}{7} m \cdot \frac{7}{9} n \cdot 6k = \frac{3}{7} \cdot \frac{7}{9} \cdot 6 mnk = 2mnk\]
  17. П) \[-6a \cdot 0.7b \cdot (-0.5c) = -6 \cdot 0.7 \cdot (-0.5) abc = 2.1abc\]
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