Question

Of the students in the band, 2/5 play a brass instrument. Of the students who play a brass instrument, 1/2 play the trumpet. What fraction of the students in the band play the trumpet?

Answer 1

Let the total number of students in the band be represented by \( N \).

First, we find the number of students who play a brass instrument:
\[
\frac{2}{5} N
\]

Next, we find the number of students who play the trumpet, which is half of those who play a brass instrument:
\[
\frac{1}{2} \left(\frac{2}{5} N\right) = \frac{2}{10} N = \frac{1}{5} N
\]

Now, to determine the fraction of the total number of students in the band who play the trumpet, we have:
\[
\frac{1}{5} N \text{ out of } N
\]

This simplifies to:
\[
\frac{1}{5}
\]

Thus, the fraction of the students in the band who play the trumpet is:
\[
\boxed{\frac{1}{5}}
\]