$\frac{7}{20} * 9 + 12 * \frac{7}{36} + 1\frac{8}{15} : 4 + \frac{3}{5} : 4\frac{1}{2} = \frac{7}{20} * \frac{9}{1} + \frac{12}{1} * \frac{7}{36} + \frac{23}{15} : 4 + \frac{3}{5} : \frac{9}{2} = \frac{7}{20} * \frac{9}{1} + \frac{12}{1} * \frac{7}{36} + \frac{23}{15} * \frac{1}{4} + \frac{3}{5} * \frac{2}{9} = \frac{63}{20} + \frac{7}{3} + \frac{23}{60} + \frac{2}{15} = (\frac{63}{20} + \frac{23}{60}) + (\frac{7}{3} + \frac{2}{15}) = \frac{63 * 3 + 23}{60} + \frac{7 * 5 + 2}{15} = \frac{189 + 23}{60} + \frac{35 + 2}{15} = \frac{212}{60} + \frac{37}{15} = \frac{212 + 37 * 4}{60} = \frac{212 + 148}{60} = \frac{360}{60} = 6$