# Two fifths of the instruments in the marching band are brass, one third are percussion, and the rest are woodwinds. What fraction of the band is woodwinds?

$\frac{4}{15}$ of the band's instruments are woodwinds.
We need a common denominator to equate the $\frac{2}{5}$, and the $\frac{1}{3}$ fractions. Clearly, we could express the fractions as $\text{fifteenths}$.
And thus $\frac{2}{5} \equiv \frac{6}{15}$, and $\frac{1}{3} \equiv \frac{5}{15}$.
The balance are woodwind instruments, i.e. $1 - \frac{6}{15} - \frac{5}{15} = \frac{4}{15}$.