3.89 Выполните действия: a) (3,4+4,3)∙3 \(\frac{4}{9}\) (8,6-5,5): \(\frac{11}{5}\) б) (\(\frac{1}{9}\) + \(\frac{5}{18}\)) + 3,125 ∙ 0,8 (\(4 \frac{5}{6}\) - 4 \(\frac{1}{3}\)): \(\frac{12}{29}\) + 23 \(\frac{1}{5}\)

3.89 Выполните действия:

a) (3,4+4,3)∙3 \(\frac{4}{9}\) (8,6-5,5): \(\frac{11}{5}\)

1) 3,4 + 4,3 = 7,7

2) 3 \(\frac{4}{9}\) = \(\frac{3 \cdot 9 + 4}{9} = \frac{31}{9}\)

3) 7,7 ∙ \(\frac{31}{9}\) = \(\frac{77}{10} \cdot \frac{31}{9} = \frac{2387}{90}\) = 26,5222...

4) 8,6 - 5,5 = 3,1

5) \(\frac{11}{5}\) = 2,2

6) 3,1 : 2,2 = \(\frac{31}{10}: \frac{22}{10} = \frac{31}{10} \cdot \frac{10}{22} = \frac{31}{22}\) = 1,409...

б) (\(\frac{1}{9}\) + \(\frac{5}{18}\)) + 3,125 ∙ 0,8 (\(4 \frac{5}{6}\) - 4 \(\frac{1}{3}\)): \(\frac{12}{29}\) + 23 \(\frac{1}{5}\)

1) \(\frac{1}{9}\) + \(\frac{5}{18}\) = \(\frac{1 \cdot 2 + 5}{18} = \frac{7}{18}\)

2) 3,125 ∙ 0,8 = 2,5

3) \(\frac{7}{18}\) + 2,5 = \(\frac{7}{18} + \frac{25}{10} = \frac{7}{18} + \frac{5}{2} = \frac{7 + 5 \cdot 9}{18} = \frac{7 + 45}{18} = \frac{52}{18} = \frac{26}{9}\) = 2,888...

4) 4 \(\frac{5}{6}\) - 4 \(\frac{1}{3}\) = \(4 + \frac{5}{6} - 4 - \frac{1}{3} = \frac{5}{6} - \frac{1}{3} = \frac{5 - 1 \cdot 2}{6} = \frac{5 - 2}{6} = \frac{3}{6} = \frac{1}{2}\)

5) \(\frac{1}{2}: \frac{12}{29} = \frac{1}{2} \cdot \frac{29}{12} = \frac{29}{24}\)

6) 23 \(\frac{1}{5}\) = \(\frac{23 \cdot 5 + 1}{5} = \frac{116}{5}\)

7) \(\frac{29}{24} + \frac{116}{5} = \frac{29 \cdot 5 + 116 \cdot 24}{120} = \frac{145 + 2784}{120} = \frac{2929}{120}\) = 24,4083...

Ответ: а) 26,5222...; 1,409... б) 2,888...; 24,4083...