There ar 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?

Three out of every eight students suggested a rainbow-themed party, so the fraction that suggested this theme is 3/8.

To find out how many students suggested a rainbow-themed party, we multiply the fraction by the total number of students:
3/8 x 40 = <<3/8*40=15>>15 students.

Therefore, 15 students suggested a rainbow-themed party.

To find out how many students did not suggest a rainbow-themed party, we subtract the students who did suggest a rainbow-themed party from the total number of students:
40 - 15 = <<40-15=25>>25 students.

Therefore, 25 students did not suggest a rainbow-themed party.

To find out how many students suggested a rainbow-themed party and how many did not, we need to use the given information that "three of every eight students suggested a rainbow-themed party."

First, let's calculate how many students represent each group of eight students:
- There are 40 students in total, and we need to divide them into groups of eight. So, the total number of groups we have is 40 divided by 8, which equals 5 groups.

Now, we can determine the number of students who suggested a rainbow-themed party by multiplying the number of groups by the given ratio of 3 out of 8:
- 5 groups x (3/8) = 15/8 = 1.875
Since we can't have a fraction of a student, we round up to the nearest whole number to get a total of 2 students who suggested a rainbow-themed party.

To find out the number of students who did not suggest a rainbow-themed party, subtract the number of students who did from the total number of students:
- Total students - Students who suggested a rainbow-themed party = Students who did not
- 40 - 2 = 38 students who did not suggest a rainbow-themed party.

So, 2 students suggested a rainbow-themed party, and 38 students did not.

To find out how many students suggested a rainbow-themed party, we can use the given information that three out of every eight students suggested this theme.

First, we need to find out how many groups of eight we can form with 40 students. We divide 40 by 8:

40 / 8 = 5

So, we can form 5 groups of eight students.

Since three students in each group of eight suggested a rainbow-themed party, we multiply 3 by the number of groups:

3 * 5 = 15

Therefore, 15 students suggested a rainbow-themed party.

To find out how many students did not suggest this theme, we subtract the number of students who did suggest it from the total number of students:

40 - 15 = 25

Therefore, 25 students did not suggest a rainbow-themed party.