There are 40 students in Joan’s class. She plans to invite them to her birthday party. She asked them to suggest a theme for her party. Three of every eight students suggested a rainbow-themed party. How many students suggested a rainbow-themed party? How many did not?
To find the number of students who suggested a rainbow-themed party, we multiply the total number of students by the fraction representing the fraction of students who suggested a rainbow-themed party: 40 students * 3/8 = <<40*3/8=15>>15 students.
To find the number of students who did not suggest a rainbow-themed party, we subtract the number who did from the total number of students: 40 students - 15 students = <<40-15=25>>25 students. Answer: \boxed{15}.