  It is well known that rational multiplication preserves normality in base
$b$. We study related normality preserving operations for the $Q$-Cantor series
expansions. In particular, we show that while integer multiplication preserves
$Q$-distribution normality, it fails to preserve $Q$-normality in a
particularly strong manner. We also show that $Q$-distribution normality is not
preserved by non-integer rational multiplication on a set of zero measure and
full Hausdorff dimension.
