$\frac{a}{3}=\frac{}{6a}=\frac{}{9a^3}=\frac{}{15b}=\frac{4a^2{c}^3}{}$
$\frac{6a}{3}=2a$, тогда:
$\frac{2a\ast <!--\; \ast \; -->a}{2a\ast <!--\; \ast \; -->3}=\frac{2a^2}{6a}$
$\frac{9a^3}{6a}=\frac{3a^2}{2}$, тогда:
$\frac{\frac{3a^2}{2}\ast <!--\; \ast \; -->2a^2}{\frac{3a^2}{2}\ast <!--\; \ast \; -->6a}=\frac{3a^4}{9a^3}$
$\frac{15b}{9a^3}=\frac{5b}{3a^3}$, тогда:
$\frac{\frac{5b}{3a^3}\ast <!--\; \ast \; -->3a^4}{\frac{5b}{3a^3}\ast <!--\; \ast \; -->9a^3}=\frac{5ab}{15b}$
$\frac{4a^2{c}^3}{5ab}=\frac{4a{c}^3}{5b}$, тогда:
$\frac{\frac{4a{c}^3}{5b}\ast <!--\; \ast \; -->5ab}{\frac{4a{c}^3}{5b}\ast <!--\; \ast \; -->15b}=\frac{4a^2{c}^3}{12a{c}^3}$
Ответ:
$\frac{a}{3}=\frac{2a^2}{6a}=\frac{3a^4}{9a^3}=\frac{5ab}{15b}=\frac{4a^2{c}^3}{12a{c}^3}$

$\frac{m}{n}=\frac{4m}{}=\frac{}{2n^2}=\frac{}{mnp}=\frac{3m^4{n}^3}{}$
$\frac{4m}{m}=4$, тогда:
$\frac{4\ast <!--\; \ast \; -->m}{4\ast <!--\; \ast \; -->n}=\frac{4m}{4n}$
$\frac{2n^2}{4n}=\frac{n}{2}$, тогда:
$\frac{\frac{n}{2}\ast <!--\; \ast \; -->4m}{\frac{n}{2}\ast <!--\; \ast \; -->4n}=\frac{2mn}{2n^2}$
$\frac{mnp}{2n^2}=\frac{mp}{2n}$, тогда:
$\frac{\frac{mp}{2n}\ast <!--\; \ast \; -->2mn}{\frac{mp}{2n}\ast <!--\; \ast \; -->2n^2}=\frac{m^{2}p}{mnp}$
$\frac{3m^4{n}^3}{m^{2}p}=\frac{3m^2{n}^3}{p}$, тогда:
$\frac{\frac{3m^2{n}^3}{p}\ast <!--\; \ast \; -->m^{2}p}{\frac{3m^2{n}^3}{p}\ast <!--\; \ast \; -->mnp}=\frac{3m^4{n}^3}{3m^3{n}^4}$
Ответ:
$\frac{m}{n}=\frac{4m}{4n}=\frac{2mn}{2n^2}=\frac{m^{2}p}{mnp}=\frac{3m^4{n}^3}{3m^3{n}^4}$