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?

Answer 1

To find the fraction of students who scored below 80% on the test, we start by defining the total number of students in the class as \( N \).

According to the problem:

• One-third of the students scored 90% or better: \[ \frac{1}{3}N \]

• Two-fifths of the students scored between 80% and 89%: \[ \frac{2}{5}N \]

Next, we compute the total fraction of students who scored either 90% or better or between 80% and 89%. We need to find common denominators to add these two fractions. The least common multiple of 3 and 5 is 15.

Convert \( \frac{1}{3} \) to a fraction with a denominator of 15: \[ \frac{1}{3} = \frac{5}{15} \]

Convert \( \frac{2}{5} \) to a fraction with a denominator of 15: \[ \frac{2}{5} = \frac{6}{15} \]

Adding these fractions gives: \[ \frac{5}{15} + \frac{6}{15} = \frac{11}{15} \]

This fraction \( \frac{11}{15} \) represents the portion of students who scored either 90% or better or between 80% and 89%.

To find the fraction of students who scored below 80%, we subtract the fraction of students who scored 90% or better and 80%-89% from 1: \[ 1 - \frac{11}{15} = \frac{15}{15} - \frac{11}{15} = \frac{4}{15} \]

Thus, the fraction of students who scored below 80% on the test is: \[ \boxed{\frac{4}{15}} \]