In Mrs. Santos' class, five-eighths of the students have nicknames, meaning that three-eighths don't have nicknames. Three-eighths of 24 is 9, so 9 students don't have nicknames.
In Mr. Russo's class, one-third of the students have nicknames, meaning that two-thirds don't have nicknames. Two-thirds of 24 is 16, so 16 students don't have nicknames.
Therefore, there are 9 students from Mrs. Santos' class and 16 students from Mr. Russo's class who don't have nicknames.
