<p>We argue that <i>per</i>-phrases like <i>two grams per liter</i> exhibit a dual interpretive pattern. When such phrases saturate predicates of quantities in simplex dimensions, like weight or distance, they are interpreted compositionally within grammar; by contrast, when referring to quantities in quotient dimensions, like density or speed, they verbalize technical notation using a type of <i>math speak</i>. Akin to mixed quotations, such verbalizations get their meanings from extra-grammatical conventions. Supporting our analysis, <i>per</i>-phrases that refer to quotient dimensions, unlike their simplex counterparts, allow meaning-preserving substitution with expressions that unambiguously verbalize technical notation. Furthermore, these same expressions are opaque to syntactic operations. Our arguments challenge the view that <i>per</i> encodes quantity division compositionally, and underscore the distinction between meanings built in grammar and those licensed by extra-grammatical conventions.</p>