#### Answer

$2\frac{1}{3}$

#### Work Step by Step

$\frac{5}{9}\times4\frac{1}{5}$ $\longrightarrow$convert mixed number
=$\frac{5}{9}\times\frac{21}{5}$ $\longrightarrow$multiply numerators and denominators
=$\frac{5\times21}{9\times5}$ $\longrightarrow$eliminate common factors
=$\frac{/\!\!5\times/\!\!3\times7}{3\times/\!\!3\times/\!\!5}$
=$\frac{7}{3}$$\longrightarrow$simplify
=$2\frac{1}{3}$