$\frac{a}{3} = \frac{}{6a} = \frac{}{9a^3} = \frac{}{15b} = \frac{4a^2c^3}{}$
$\frac{6a}{3} = 2a$, тогда:
$\frac{2a * a}{2a * 3} = \frac{2a^2}{6a}$
$\frac{9a^3}{6a} = \frac{3a^2}{2}$, тогда:
$\frac{\frac{3a^2}{2} * 2a^2}{\frac{3a^2}{2} * 6a} = \frac{3a^4}{9a^3}$
$\frac{15b}{9a^3} = \frac{5b}{3a^3}$, тогда:
$\frac{\frac{5b}{3a^3} * 3a^4}{\frac{5b}{3a^3} * 9a^3} = \frac{5ab}{15b}$
$\frac{4a^2c^3}{5ab} = \frac{4ac^3}{5b}$, тогда:
$\frac{\frac{4ac^3}{5b} * 5ab}{\frac{4ac^3}{5b} * 15b} = \frac{4a^2c^3}{12ac^3}$
Ответ:
$\frac{a}{3} = \frac{2a^2}{6a} = \frac{3a^4}{9a^3} = \frac{5ab}{15b} = \frac{4a^2c^3}{12ac^3}$

$\frac{m}{n} = \frac{4m}{} = \frac{}{2n^2} = \frac{}{mnp} = \frac{3m^4n^3}{}$
$\frac{4m}{m} = 4$, тогда:
$\frac{4 * m}{4 * n} = \frac{4m}{4n}$
$\frac{2n^2}{4n} = \frac{n}{2}$, тогда:
$\frac{\frac{n}{2} * 4m}{ \frac{n}{2} * 4n} = \frac{2mn}{2n^2}$
$\frac{mnp}{2n^2} = \frac{mp}{2n}$, тогда:
$\frac{\frac{mp}{2n} * 2mn}{\frac{mp}{2n} * 2n^2} = \frac{m^2p}{mnp}$
$\frac{3m^4n^3}{m^2p} = \frac{3m^2n^3}{p}$, тогда:
$\frac{\frac{3m^2n^3}{p} * m^2p}{\frac{3m^2n^3}{p} * mnp} = \frac{3m^4n^3}{3m^3n^4}$
Ответ:
$\frac{m}{n} = \frac{4m}{4n} = \frac{2mn}{2n^2} = \frac{m^2p}{mnp} = \frac{3m^4n^3}{3m^3n^4}$