1) \(4\frac{1}{3} \cdot 6 - 1\frac{23}{42} \cdot 13 + 2\frac{1}{8} \cdot \frac{29}{51} = \frac{13}{3} \cdot 6 - \frac{65}{42} \cdot 13 + \frac{17}{8} \cdot \frac{29}{51} = 26 - \frac{845}{42} + \frac{29}{24} = 26 - 20.12 + 1.21 \approx 7.09\)
2) \((\frac{5}{10} - 3\frac{4}{13}) \cdot \frac{5}{38} + \frac{9}{84} \div 12\frac{1}{15} = (\frac{1}{2} - \frac{43}{13}) \cdot \frac{5}{38} + \frac{3}{28} \div \frac{181}{15} = (\frac{13}{26} - \frac{86}{26}) \cdot \frac{5}{38} + \frac{3}{28} \cdot \frac{15}{181} = (-\frac{73}{26}) \cdot \frac{5}{38} + \frac{45}{5068} = -\frac{365}{988} + \frac{45}{5068} \approx -0.369 + 0.009 = -0.36\)
3) \((3\frac{1}{3})^2 - 2\frac{13}{16} \cdot 2\frac{5}{2} = (\frac{10}{3})^2 - \frac{45}{16} \cdot \frac{9}{2} = \frac{100}{9} - \frac{405}{32} = \frac{3200 - 3645}{288} = -\frac{445}{288} \approx -1.54\)
4) \((\frac{5}{12} + \frac{13}{20}) \cdot 1\frac{13}{32} = (\frac{25}{60} + \frac{39}{60}) \cdot \frac{45}{32} = \frac{64}{60} \cdot \frac{45}{32} = \frac{16}{15} \cdot \frac{45}{32} = \frac{1}{1} \cdot \frac{3}{2} = \frac{3}{2} = 1.5\)