1/6 of the students are athletes. 5/7 of the athletes play in the fall. What fraction of the students are athletes that also play in the fall?

Question

______________ are athletes that also play in the fall.

Answer 1

To determine what fraction of the students are athletes that also play in the fall, we can follow these steps:

1. Let the total number of students be represented by 1 (this is our whole).
2. The fraction of students that are athletes is given as \( \frac{1}{6} \).
3. Among the athletes, \( \frac{5}{7} \) participate in the fall.

Now, to find the fraction of the total students that are athletes playing in the fall, we multiply these two fractions:

\[ \text{Fraction of students who are athletes playing in the fall} = \left(\frac{1}{6}\right) \times \left(\frac{5}{7}\right) \]

Calculating this gives:

\[ \frac{1}{6} \times \frac{5}{7} = \frac{1 \times 5}{6 \times 7} = \frac{5}{42} \]

Thus, the fraction of the students who are athletes that also play in the fall is \( \frac{5}{42} \).

So, the final answer is:

\(\frac{5}{42}\) are athletes that also play in the fall.