Question

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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?

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Answer 1

4/15 is the answer

Answer 2

To find the fraction of students who scored below 80% on the test, we need to first determine the total fraction of students that scored 90% or better, and those that scored between 80% and 89%.

1. **Fraction of students scoring 90% or better**: \( \frac{1}{3} \)
2. **Fraction of students scoring between 80% and 89%**: \( \frac{2}{5} \)

To find the fraction of students who scored below 80%, we can first add the two fractions together and then subtract from 1 (which represents the whole class).

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

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

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

3. Add the two fractions together:
\[
\frac{5}{15} + \frac{6}{15} = \frac{11}{15}
\]

4. Subtract the sum from 1 to find the fraction of students who scored below 80%:
\[
1 - \frac{11}{15} = \frac{15}{15} - \frac{11}{15} = \frac{4}{15}
\]

Therefore, the fraction of students who scored below 80% on the test is \( \frac{4}{15} \).

Answer 3

Yes, that's correct! The fraction of students who scored below 80% on the test is \( \frac{4}{15} \). If you have any more questions or need further assistance, feel free to ask!