Convert both mixed numbers to improper fractions with a common denominator, then subtract.<br><br>
&bull; \( 2\frac{1}{5} = \frac{11}{5} = \frac{99}{45} \)<br>
&bull; \( 1\frac{2}{9} = \frac{11}{9} = \frac{55}{45} \)<br>
&bull; \( \frac{99}{45} - \frac{55}{45} = \frac{44}{45} \)<br>
&bull; \( \frac{44}{45} \) is already in simplest form (HCF of 44 and 45 is 1).<br>
&bull; Since the numerator (44) is less than the denominator (45), the answer is a proper fraction, not a mixed number.<br><br>
Final Answer: C: \( \frac{44}{45} \)