$\frac{3}{5} * \frac{1}{2} * \frac{4}{9} = \frac{3 * 1 * 4}{5 * 2 * 9} = \frac{1 * 1 * 2}{5 * 1 * 3} = \frac{2}{15}$

$\frac{4}{5} * \frac{10}{27} * \frac{15}{16} = \frac{4 * 10 * 15}{5 * 27 * 16} = \frac{1 * 2 * 5}{1 * 9 * 4} = \frac{1 * 5 * 1}{1 * 9 * 2} = \frac{5}{18}$

$\frac{1}{2} * \frac{2}{3} * \frac{3}{4} * \frac{4}{5} = \frac{1 * 2 * 3 * 4}{2 * 3 * 4 * 5} = \frac{1}{5}$

$\frac{6}{7} * \frac{7}{8} * \frac{8}{9} * \frac{9}{10} * \frac{10}{11} = \frac{6 * 7 * 8 * 9 * 10}{7 * 8 * 9 * 10 * 11} = \frac{6}{11}$

$\frac{4}{7} * \frac{35}{36} * \frac{3}{5} = \frac{4 * 35 * 3}{7 * 36 * 5} = \frac{1 * 5 * 3}{1 * 9 * 5} = \frac{1 * 1 * 1}{1 * 3 * 1} = \frac{1}{3}$

$\frac{1}{2} * \frac{2}{3} * \frac{3}{4} * ... * \frac{23}{24} * \frac{24}{25} = \frac{1 * 2 * 3 * ... * 23 * 24}{2 * 3 * 4 * ... * 24 * 25} = \frac{1 * 1 * 1 * ... * 1 * 1}{1 * 1 * 1 * ... * 1 * 25} = \frac{1}{25}$