$\frac{a + 1}{7x} * \frac{2x}{a + 1} = \frac{1}{7} * \frac{2}{1} = \frac{2}{7}$

$\frac{2m}{m - n} : \frac{3mn}{m - n} = \frac{2m}{m - n} * \frac{m - n}{3mn} = \frac{2}{1} * \frac{1}{3n} = \frac{2}{3n}$

$\frac{4p}{p - 3} * \frac{p - 3}{2p^2} = \frac{2}{1} * \frac{1}{p} = \frac{2}{p}$

$\frac{x + y}{8a} : \frac{x + y}{16a^2b} = \frac{x + y}{8a} * \frac{16a^2b}{x + y} = \frac{1}{1} * \frac{2ab}{1} = 2ab$

$\frac{2x + 2y}{3} * \frac{6}{x + y} = \frac{2(x + y)}{3} * \frac{6}{x + y} = \frac{2}{1} * \frac{2}{1} = 4$

$\frac{4a}{a^2b} : \frac{5ab}{3a - 3b} = \frac{4a}{a^2b} * \frac{3a - 3b}{5ab} = \frac{4a}{a^2b} * \frac{3(a - b)}{5ab} = \frac{4}{a^2b} * \frac{3(a - b)}{5b} = \frac{12(a - b)}{5a^2b^2}$

$\frac{m - 3n}{6m} * \frac{3mn}{4m - 12n} = \frac{m - 3n}{6m} * \frac{3mn}{4(m - 3n)} = \frac{1}{2} * \frac{n}{4} = \frac{n}{8}$

$\frac{2p - 4q}{3p^2} : \frac{3p - 6q}{4pq} = \frac{2p - 4q}{3p^2} * \frac{4pq}{3p - 6q} = \frac{2(p - 2q)}{3p^2} * \frac{4pq}{3(p - 2q)} = \frac{2}{3p} * \frac{4q}{3} = \frac{8q}{9p}$

$\frac{ax - ay}{cd} * \frac{cx + cy}{x - y} = \frac{a(x - y)}{cd} * \frac{c(x + y)}{x - y} = \frac{a}{d} * \frac{x + y}{1} = \frac{a(x + y)}{d}$

$\frac{mk}{am - an} : \frac{ka - k}{2m - 2n} = \frac{mk}{am - an} * \frac{2m - 2n}{ka - k} = \frac{mk}{a(m - n)} * \frac{2(m - n)}{k(a - 1)} = \frac{m}{a} * \frac{2}{a - 1} = \frac{2m}{a(a - 1)}$