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

б) Выполним действия:

1) $$\frac{1}{9} \cdot \frac{5}{18} = \frac{1 \cdot 5}{9 \cdot 18} = \frac{5}{162}$$

2) $$3,125 \cdot 0,8 = 2,5$$

3) $$\frac{5}{162} + 2,5 = \frac{5}{162} + \frac{25}{10} = \frac{5}{162} + \frac{5}{2} = \frac{5 + 5 \cdot 81}{162} = \frac{5 + 405}{162} = \frac{410}{162} = \frac{205}{81}$$

4) $$4\frac{5}{6} - 4\frac{1}{3} = \frac{4 \cdot 6 + 5}{6} - \frac{4 \cdot 3 + 1}{3} = \frac{24 + 5}{6} - \frac{12 + 1}{3} = \frac{29}{6} - \frac{13}{3} = \frac{29 - 13 \cdot 2}{6} = \frac{29 - 26}{6} = \frac{3}{6} = \frac{1}{2}$$

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

6) $$\frac{205}{81} : \frac{29}{24} = \frac{205}{81} \cdot \frac{24}{29} = \frac{205 \cdot 24}{81 \cdot 29} = \frac{4920}{2349} = \frac{1640}{783}$$

7) $$23\frac{4}{5} = \frac{23 \cdot 5 + 4}{5} = \frac{115 + 4}{5} = \frac{119}{5}$$

8) $$\frac{1640}{783} + \frac{119}{5} = \frac{1640 \cdot 5 + 119 \cdot 783}{783 \cdot 5} = \frac{8200 + 93177}{3915} = \frac{101377}{3915} = 25\frac{3552}{3915} = 25\frac{1184}{1305}$$

Ответ: $$\frac{101377}{3915} = 25\frac{1184}{1305}$$