Final answer:
The ancient Aztecs used a 260-day ritual calendar and a 365-day solar calendar, which in combination, completed a full 52-year cycle known as the calendar round.
Step-by-step explanation:
The ancient Aztecs incorporated two primary calendars into their understanding of time: the 260-day ritual calendar and the 365-day solar calendar. These two calendars were essential to Mesoamerican cultures, where the 260-day calendar, consisting of 20 months with 13 days each, was used for rituals and ceremonies, while the 365-day calendar, having 18 months of 20 days with five additional nameless days, focused on agricultural planning.
Both of these calendars would interlock in a cycle called the calendar round, completing a full 52-year cycle that was commemorated by special rituals such as the New Fire Ceremony among the Mexica. The Maya culture also developed the Long Count Calendar for tracking even longer periods.
Tracking major astronomical events, the calendars played a significant role in the timing of rituals and possibly even battles.