Find the total number of parts, then express the longest piece as a fraction of the total.<br><br>
&bull; Pieces ratio = \(2 : 4 : 9\)<br>
&bull; Total parts = \(2 + 4 + 9 = 15\)<br>
&bull; Longest piece = 9 parts<br>
&bull; \(\frac{9}{15} = \frac{3}{5}\)<br><br>
Final Answer: a = 3, b = 5