3/4 of a class of 32 students
study English and 3/8 study
mathematics. Every student
studies at least one of these
subjects. What fraction of the
class study mathematics but not
English?
A. 3/4
B. 5/8
C. 3/8
D. 8/9
To find the fraction of the class that studies mathematics but not English, we need to subtract the fraction that studies both subjects from the fraction that studies only mathematics.
Given that 3/4 of the class studies English, we can find the fraction that studies both subjects by multiplying 3/4 by 3/8:
(3/4) * (3/8) = 9/32
So, 9/32 of the class studies both subjects.
To find the fraction that studies only mathematics, we need to subtract 9/32 from the fraction that studies only mathematics and English. We know that the total fraction that studies mathematics is 3/8. So, to find the fraction that studies only mathematics, we subtract 9/32 from 3/8:
(3/8) - (9/32) = (6/32) - (9/32) = -3/32
Since the fraction cannot be negative, we know that at least one error has been made in the problem or the calculations. Therefore, the given answer choices do not accurately represent the situation.
To find the fraction of the class that studies mathematics but not English, we need to subtract the fraction of the class that studies both subjects from the fraction of the class that studies mathematics.
First, let's determine how many students study English and how many students study mathematics.
Given that 3/4 of the class (32 students) study English, we can find the number of students studying English by multiplying 3/4 by 32:
(3/4) * 32 = 24
Therefore, 24 students study English.
Given that 3/8 of the class (32 students) study mathematics, we can find the number of students studying mathematics by multiplying 3/8 by 32:
(3/8) * 32 = 12
Therefore, 12 students study mathematics.
Next, let's determine how many students study both subjects:
Since every student studies at least one of these subjects, the number of students studying both subjects can be found by subtracting the number of students studying English from the total number of students:
32 - 24 = 8
Therefore, 8 students study both English and mathematics.
Finally, let's determine the fraction of the class that studies mathematics but not English:
To find this, we subtract the fraction of the class that studies both subjects (8 students) from the fraction of the class that studies mathematics (12 students):
(12 - 8) / 32 = 4 / 32 = 1 / 8
Therefore, 1/8 of the class studies mathematics but not English.
The correct answer is C. 3/8.