### Primitive substitutive numbers are closed under rational multiplication

Let $M\left(r\right)$ denote the set of real numbers $\alpha $ whose base-$r$ digit expansion is ultimately primitive substitutive, i.e., contains a tail which is the image (under a letter to letter morphism) of a fixed point of a primitive substitution. We show that the set $M\left(r\right)$ is closed under multiplication by rational numbers, but not closed under addition.