To find the number of students in the art club, we need to first find  the number of students in the science club:

First set of 3 elements:

From “The number of students in a math club is 8/5 of the number of students in a science club”,  ” the number of students in the science club” is the noun phrase after  8/5 of”  so  the number of students in the science club is the amount in 1 (whole). The fraction is 8/5; the amount in the fraction, 8/5, is 8.

the first set of the 3 elements:

The amount in 1: the number of students in the science club?

The fraction: 8/5

The amount in the fraction: 8, students

The amount in 1= the amount in the fraction ÷ the fraction=8÷8/5= 8 x5/8 =5 students

There are 5 students in the science club.

Second set of 3 elements:

We divide the fractional part, , into the amount in this part, 5, to find the amount in 1 (whole), the number of students in the art club:

5÷= 5 x 3=15 students

Now we are ready to find the number of students in the art club.

Second set of 3 elements:

From” the number of students in the science club is 1/3 of the number of students in an art club”, the noun phrase after “1/3 of” is “ the number of students in the art club” so the number of students in the art club is the amount in 1; the fraction is 1/3; the amount in the fraction is the number of students in the science club, 5.

The following is the 2nd set of the 3 elements:

The amount in 1: the number of students in the art club?

The fraction: 1/3

The amount in the fraction: 5 students

The number of students in the art club=The amount in 1= the amount in a fraction ÷ the fraction= 5÷1/3= 5 x 3=15 students