Answer
False
Work Step by Step
To determine if a proportion is true, we have to find if the cross products are equal.
The cross products of $\frac{a}{b}=\frac{c}{d}$ are $a \cdot d$ and $b \cdot c$.
$2\frac{2}{5} = \frac{12}{5}$
$\frac{12}{5}*\frac{1}{4} = \frac{3}{5}, \frac{10}{9}*\frac{2}{3} = \frac{20}{27}, \frac{3}{5} \neq \frac{20}{27} \rightarrow$ false