Complex sentence: Rat Terriers were cherished as loyal hunting companions and efficient killers of vermin on 20th century American farms: as a result, they were one of the most popular dog types from the 1920s to the 1940s.
Split into simpler sentences: Rat Terriers were cherished as loyal and efficient killers of vermin on 20th century American Farms, as well as excellent hunting companions. As a result they were one of the most popular dog types from the 1920s to the 1940s.