Let's define the total number of students in the class as \( N \).
According to the problem:
-
One third of the students scored 90% or better, which can be represented as: \[ \text{Students scoring 90% or better} = \frac{1}{3}N \]
-
Two fifths of the students scored between 80% and 89%, represented as: \[ \text{Students scoring 80% to 89%} = \frac{2}{5}N \]
To find how many students scored below 80%, we need to compute the total number of students who scored either 90% or better or between 80% and 89%.
First, we add the fractions: \[ \frac{1}{3}N + \frac{2}{5}N \]
To add the fractions, we need a common denominator. The least common multiple of 3 and 5 is 15.
Converting the fractions: \[ \frac{1}{3} = \frac{5}{15} \quad \text{and} \quad \frac{2}{5} = \frac{6}{15} \]
Adding these results: \[ \frac{5}{15}N + \frac{6}{15}N = \frac{11}{15}N \]
This means that \(\frac{11}{15}N\) students scored 80% or better.
The rest of the students scored below 80%. To find this fraction, we subtract the above result from the total number of students: \[ N - \frac{11}{15}N = \frac{15}{15}N - \frac{11}{15}N = \frac{4}{15}N \]
Thus, the fraction of the students who scored below 80% on the test is: \[ \frac{4}{15} \]
1 answer