Rather than working memory capacity acting as a distinct subordinate function of fluid intelligence, there is an emerging consensus that their relationship can be understood as an outcome of common functions dictated by the strength and flexibility of bindings which integrate representations relationally. The current study considers the Arithmetic Chain Task (Oberauer, Demmrich, Mayr, & Kliegl, 2001) which contrasts access (integrating previously stored information for use in the arithmetic processing) against mere retention (holding previously stored information for recall after the arithmetic processing). Participants (n = 122) completed the Arithmetic Chain Task (ACT) with a novel manipulation that split the access condition into fixed-order vs. random-order access. Both forms of access require integration of previously stored information into the arithmetic, but random-order access restricts systematic chunking, necessitating multiple flexible bindings that can be updated in light of new information. Participants also completed a measure of working memory and a measure of fluid intelligence. Results replicated Oberauer et al.'s findings on a demarcation between retention and access, though the current data indicate that random-order presentation is necessary to distinguish access from retention. Crucially, this random-order access is also required to link the ACT to a factor representing the commonality in WM and Gf. These results suggest that what is common to WM and Gf is the capacity to maintain multiple durable and flexible bindings.