The reciprocal of $(2 / 5) \times(-4 / 9)$ is__________.
$=(2 \times-4) /(5 \times 9)$
$=-8 / 45$
Reciprocal $=-45 / 8$
Hence, the reciprocal of $(2 / 5) \times(-4 / 5)$ is $\underline{-45 / 8}$.
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