Final answer:
The world during the time when the first primate-like animals lived saw the evolution of primates, the emergence of modern rain forests and grasslands, and the abundance and spread of flowering plants and insects.
Step-by-step explanation:
The first true primates, resembling present-day prosimians such as lemurs, appeared around 55 million years ago in the Eocene epoch. They were found in North America, Europe, Asia, and Africa. Evolutionary changes continued in these early primates, with larger brains and eyes, and smaller muzzles being the trend.
By the end of the Eocene epoch, many of the early prosimian species went extinct due to cooler temperatures or competition from the first monkeys. The primates during this time had adaptations for climbing trees, large brains relative to body size, and stereoscopic vision.
Overall, the world during the time when the first primate-like animals lived saw the evolution of primates, the emergence of modern rain forests and grasslands, and the abundance and spread of flowering plants and insects.