$1\frac{3}{4} * 2\frac{4}{7} : 4\frac{1}{2} + 2\frac{2}{5} : \frac{9}{10} * \frac{3}{8} = \frac{7}{4} * \frac{18}{7} : \frac{9}{2} + \frac{12}{5} : \frac{9}{10} * \frac{3}{8} = \frac{7}{4} * \frac{18}{7} * \frac{2}{9} + \frac{12}{5} * \frac{10}{9} * \frac{3}{8} = \frac{7}{2 * 2} + \frac{9 * 2}{7} * \frac{2}{9} + \frac{4 * 3}{5} * \frac{5 * 2}{3 * 3} * \frac{3}{4 * 2} = 1 + 1 = 2$