Let's denote the total number of students in the class as \( N \).
-
Students who scored 90% or better:
\[ \frac{1}{3}N \] -
Students who scored between 80% and 89%:
\[ \frac{2}{5}N \]
Now, to find the fraction of students that scored below 80%, we first need to determine the total fraction of students accounted for by those who scored 90% or better and those who scored between 80% and 89%.
Adding these two fractions: \[ \frac{1}{3} + \frac{2}{5} \]
To add these fractions, we need a common denominator. The least common multiple of 3 and 5 is 15.
Converting each fraction:
\[
\frac{1}{3} = \frac{5}{15} \quad \text{and} \quad \frac{2}{5} = \frac{6}{15}
\]
Now, adding them: \[ \frac{5}{15} + \frac{6}{15} = \frac{11}{15} \]
This means that \( \frac{11}{15} \) of the students scored 90% or better or between 80% and 89%.
To find the fraction of students who scored below 80%, we subtract this result from 1: \[ 1 - \frac{11}{15} = \frac{15}{15} - \frac{11}{15} = \frac{4}{15} \]
Therefore, the fraction of students who scored below 80% on the test is: \[ \boxed{\frac{4}{15}} \]
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