Consider these Latin cardinal numbers: quadrAginta, quinquAginta, sexAginta, nonAginta. The -ginta seems to stand for tens (cf. triginta, octoginta) and the initial parts quadr-, quinqu-, sex-, and non- are easy to connect with 4, 5, 6, and 9, respectively. The thing that puzzles me is the A in between (capitalized in the examples). What is the origin of this A? Do we know if it has a role or meaning? Is it related to the other long A at the end? I don't recall seeing a similar A binding two words together in a similar fashion in any other context.
This is a messy point in Indo-European studies. Most of the many who have written on it think that the internal long ā originated in quadrāgintā and then spread by analogy to sexāgintā etc. The -rā- in quadrāgintā is then explained as the reflex of long syllabic /ṝ/, or as /r/ plus a laryngeal, or something like that. It is discussed in Sihler and de Vaan, in both cases somewhat differently, but along these general lines.