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Recall that, to compute the product of two fractions, we use the following rule:
[tex]\frac{a}{b}\times\frac{c}{d}=\frac{a\times c}{b\times d}\text{.}[/tex]Therefore,
[tex]\frac{1}{6}\times\frac{2}{5}=\frac{1\times2}{6\times5}\text{.}[/tex]Simplifying the above result, we get:
[tex]\frac{1}{6}\times\frac{2}{5}=\frac{2}{30}=\frac{1}{15}\text{.}[/tex]Answer:
[tex]\frac{1}{15}\text{.}[/tex]