6.44 Выполните действия: a) (8\(\frac{4}{5}\) : 8 - 6,016 \(\cdot\) 0,375 - \(\frac{2}{35}\) \(\cdot\) 0,07) : 1\(\frac{4}{25}\); b) (5\(\frac{7}{20}\) - 3,66) : 1\(\frac{6}{7}\) + (4\(\frac{5}{8}\) - 1\(\frac{1}{4}\)) : 0,625; в) \(80,6 \cdot 42,2 – 330,52\) \(\cdot\) (298,53 : 27,9) – 857,56.

Решение:

1. а) Вычисляем по действиям:
   • \( 8\(\frac{4}{5}\) = \(\frac{44}{5}\) \)
   • \( \frac{44}{5} : 8 = \frac{44}{5 \cdot 8} = \frac{11}{10} = 1.1 \)
   • \( 6,016 \cdot 0,375 = 2.256 \)
   • \( \frac{2}{35} \cdot 0,07 = \frac{2}{35} \cdot \frac{7}{100} = \frac{2}{5 \cdot 100} = \frac{1}{250} = 0.004 \)
   • \( 1.1 - 2.256 - 0.004 = 1.1 - 2.26 = -1.16 \)
   • \( 1\(\frac{4}{25}\) = \(\frac{29}{25}\) = 1.16 \)
   • \( -1.16 : 1.16 = -1 \)
2. б) Вычисляем по действиям:
   • \( 5\(\frac{7}{20}\) = \(\frac{107}{20}\) = 5.35 \)
   • \( 5.35 - 3.66 = 1.69 \)
   • \( 1\(\frac{6}{7}\) = \(\frac{13}{7}\) \)
   • \( 1.69 : \frac{13}{7} = \frac{169}{100} \cdot \frac{7}{13} = \frac{13 \cdot 7}{100} = \frac{91}{100} = 0.91 \)
   • \( 4\(\frac{5}{8}\) = \(\frac{37}{8}\) = 4.625 \)
   • \( 1\(\frac{1}{4}\) = \(\frac{5}{4}\) = 1.25 \)
   • \( 4.625 - 1.25 = 3.375 \)
   • \( 3.375 : 0.625 = \frac{3375}{1000} : \frac{625}{1000} = \frac{3375}{625} = 5.4 \)
   • \( 0.91 + 5.4 = 6.31 \)
3. в) Вычисляем по действиям:
   • \( 80.6 \cdot 42.2 = 3401.32 \)
   • \( 3401.32 - 330.52 = 3070.8 \)
   • \( 298.53 : 27.9 = 10.7 \)
   • \( 3070.8 \cdot 10.7 = 32857.56 \)
   • \( 32857.56 - 857.56 = 32000 \)

Ответ: а) -1; б) 6,31; в) 32000.