1) 3 \frac{5}{6} * 1 \frac{7}{23} = \frac{3 * 6 + 5}{6} * \frac{1 * 23 + 7}{23} = \frac{23}{6} * \frac{30}{23} = \frac{23 * 30}{6 * 23} = \frac{30}{6} = 5.
2) \frac{22}{35} * \frac{21}{44} = \frac{22 * 21}{35 * 44} = \frac{22 * 3 * 7}{5 * 7 * 22 * 2} = \frac{3}{5 * 2} = \frac{3}{10}.
3) 36 * \frac{7}{9} = \frac{36 * 7}{9} = \frac{4 * 9 * 7}{9} = 4 * 7 = 28.