One-third of the students in class scored 90% or better on a test. Two-fifths of the students scored 80% - 89% on the test. The rest of the students scored below 80% on the test. What fraction of the students scored below 80% on the test? Desmos Scientific Calculator (To open the calculator in a new window, remember to hold Ctrl before selecting this link.) (1 point) Enter your response a FRACTION to receive credit for this problem.

Answer 1

Let the total number of students in the class be \( x \).

1. The fraction of students who scored 90% or better is \( \frac{1}{3}x \).
2. The fraction of students who scored between 80% and 89% is \( \frac{2}{5}x \).

To find the fraction of students who scored below 80%, we first need to sum the fractions of the two groups of students:

\[ \text{Total fraction of students who scored 90% or better and 80% - 89%} = \frac{1}{3} + \frac{2}{5} \]

To add these fractions, we need a common denominator. The least common multiple of 3 and 5 is 15.

Convert each fraction:

\[ \frac{1}{3} = \frac{5}{15} \] \[ \frac{2}{5} = \frac{6}{15} \]

Now, we can add them together:

\[ \frac{5}{15} + \frac{6}{15} = \frac{11}{15} \]

This means that \( \frac{11}{15} \) of the students scored 90% or better and between 80% - 89%.

To find the fraction of students who scored below 80%, we subtract this sum from 1:

\[ \text{Fraction of students who scored below 80%} = 1 - \frac{11}{15} = \frac{15}{15} - \frac{11}{15} = \frac{4}{15} \]

Thus, the fraction of students who scored below 80% on the test is

\[ \boxed{\frac{4}{15}}. \]