Answer
$\frac{2}{5}$
Work Step by Step
$\frac{16\times9\times4}{15\times8\times12}\longrightarrow$ Rewrite each factor as a product of its prime factors.
$\frac{(2\times2\times2\times2)(3\times3)(2\times2)}{(3\times5)(2\times2\times2)(2\times2\times3)}\longrightarrow$ Reorder the factors from smallest to largest to help find those than can cancel.
$\frac{2\times2\times2\times2\times2\times2\times3\times3}{2\times2\times2\times2\times2\times3\times3\times5}\longrightarrow$ Identify factors that appear in both numerator and denominator (indicated by the line over the top).
$\frac{\overline{2\times2\times2\times2\times2}\times2\times\overline{3\times3}}{\overline{2\times2\times2\times2\times2\times3\times3}\times5}\longrightarrow$ Eliminate factors that cancel.
$\frac{2}{5}$
