Let's denote the total number of students in the class as \( x \).
According to the problem:
- One third of the students scored 90% or better: \( \frac{1}{3}x \)
- Two fifths of the students scored 80%-89%: \( \frac{2}{5}x \)
To find the fraction of students who scored below 80%, we first need to add the fractions of students who scored 90% or better and those who scored 80%-89%.
We need a common denominator to add these fractions. The least common multiple of 3 and 5 is 15. We can convert the fractions as follows:
- \( \frac{1}{3} = \frac{5}{15} \)
- \( \frac{2}{5} = \frac{6}{15} \)
Now, we can add these two fractions:
\[ \frac{5}{15} + \frac{6}{15} = \frac{11}{15} \]
This means that \( \frac{11}{15} \) of the students scored either 90% or better or 80%-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 \( \frac{4}{15} \).