$\frac{a}{b}\ast <!--\; \ast \; -->\frac{c}{d}=\frac{aс}{bd}$

$\frac{x}{y}:\frac{a}{b}=\frac{x}{y}\ast <!--\; \ast \; -->\frac{b}{a}=\frac{bx}{ay}$

$\frac{4a}{7b}\ast <!--\; \ast \; -->\frac{21}{a}=\frac{4}{b}\ast <!--\; \ast \; -->\frac{3}{1}=\frac{12}{b}$

$\frac{5}{8}:\frac{15q}{16p}=\frac{5}{8}\ast <!--\; \ast \; -->\frac{16p}{15q}=\frac{2p}{3q}$

$\frac{5ax}{6by}\ast <!--\; \ast \; -->\frac{3x}{5y}=\frac{ax}{2by}\ast <!--\; \ast \; -->\frac{x}{y}=\frac{a{x}^2}{2b{y}^2}$

$\frac{7}{a}\ast <!--\; \ast \; -->\frac{5ax}{14by}=\frac{5x}{2by}$

$\frac{8a^{2}y}{5bx}:\frac{3ay}{4b^{2}x}=\frac{8a^{2}y}{5bx}\ast <!--\; \ast \; -->\frac{4b^{2}x}{3ay}=\frac{8a}{5}\ast <!--\; \ast \; -->\frac{4b}{3}=\frac{32ab}{15}$

$\frac{25x^2{y}^3}{36ab}:\frac{35x^{3}y}{24b^2}=\frac{25x^2{y}^3}{36ab}\ast <!--\; \ast \; -->\frac{24b^2}{35x^{3}y}=\frac{5y^2}{3a}\ast <!--\; \ast \; -->\frac{2b}{7x}=\frac{10b{y}^2}{21ax}$