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?

Question

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Answer 1

Let's denote the total number of students in the class as \( S \).

According to the problem:

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

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

Now, we need to determine the fraction of students who scored below 80%. To do this, we can first combine the fractions that correspond to the students scoring 90% or better and those scoring between 80% and 89%.

To find a common denominator, we can use 15 (the least common multiple of 3 and 5):

• Convert \(\frac{1}{3} S\) to have a denominator of 15: \[ \frac{1}{3} S = \frac{5}{15} S \]
• Convert \(\frac{2}{5} S\) to have a denominator of 15: \[ \frac{2}{5} S = \frac{6}{15} S \]

Now we can combine these fractions: \[ \frac{5}{15} S + \frac{6}{15} S = \frac{11}{15} S \]

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

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

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