$$k\times\frac{24}{9}=\frac{26}{91}\times\frac{14}{13}$$
$k=\frac{3}{26}\approx 0.115384615$
$$k\times \frac{8}{3}=\frac{26}{91}\times \frac{14}{13}$$
$$k\times \frac{8}{3}=\frac{2}{7}\times \frac{14}{13}$$
$$k\times \frac{8}{3}=\frac{2\times 14}{7\times 13}$$
$$k\times \frac{8}{3}=\frac{28}{91}$$
$$k\times \frac{8}{3}=\frac{4}{13}$$
$$k=\frac{4}{13}\times \frac{3}{8}$$
$$k=\frac{4\times 3}{13\times 8}$$
$$k=\frac{12}{104}$$
$$k=\frac{3}{26}$$
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