During one year in school 5\8 of the students had measles 1\2 had chickenpok and 1\8 had neither. What fraction of the school had both measles and chickenpok?
5/8 + 1/2 - x = 1 - 1/8
To find the fraction of students in the school who had both measles and chickenpox, we can subtract the fractions of students who had only measles and only chickenpox from the total number of students.
Let's denote the total fraction of students as 1.
Given that 5/8 of the students had measles and 1/2 had chickenpox, we can represent this information as follows:
Fraction of students with measles = 5/8
Fraction of students with chickenpox = 1/2
We are also given that 1/8 of the students had neither measles nor chickenpox.
Thus, the fraction of students who had either measles or chickenpox or both can be calculated as follows:
Fraction of students with either measles or chickenpox = Fraction of students with measles + Fraction of students with chickenpox - Fraction of students with neither measles nor chickenpox
= 5/8 + 1/2 - 1/8
To simplify this fraction, we need to find a common denominator, which is 8.
= (5/8) + (4/8) - (1/8)
= 9/8
Since the fraction is greater than 1, it means that some students were counted twice. Therefore, the fraction of students who had both measles and chickenpox is:
Fraction of students with both measles and chickenpox = Fraction of students with measles + Fraction of students with chickenpox - Fraction of students with neither measles nor chickenpox - 1
= 9/8 - 1
= 8/8
Therefore, the fraction of the school that had both measles and chickenpox is 8/8, which simplifies to 1 whole.
To find the fraction of students who had both measles and chickenpox, we need to analyze the given information.
Let's assume the total number of students in the school is represented by "x".
Given that 5/8 of the students had measles, we can calculate the number of students with measles as (5/8) * x.
Similarly, if 1/2 of the students had chickenpox, the number of students with chickenpox will be (1/2) * x.
Now, the fraction of students who had neither measles nor chickenpox is given as 1/8. Therefore, the number of students with neither measles nor chickenpox is (1/8) * x.
Since the number of students who had measles and chickenpox is not explicitly given, let's assume it as "y".
Accordingly, the number of students who had both measles and chickenpox would be (5/8) * x + (1/2) * x - (1/8) * x - y (subtracting the number of students who had neither from the total number).
Now, we want to find the fraction of students with both measles and chickenpox, so we need to express the number of students with both measles and chickenpox as a fraction of the total number of students, x.
That fraction would be: y/x.
Therefore, the answer is y/x.