Solve for \( a \) \[ \begin{array}{l}\frac{1}{9}=\frac{a}{6} \\ a=\frac{6}{54}\end{array} \]

To solve for \( a \) in the first equation, we can cross-multiply: \[ 1 \cdot 6 = 9 \cdot a \] This simplifies to: \[ 6 = 9a \] Next, we can isolate \( a \) by dividing both sides by 9: \[ a = \frac{6}{9} \] Now, simplifying \( \frac{6}{9} \): \[ a = \frac{2}{3} \] Now let’s check the second equation given: \[ a = \frac{6}{54} \] Simplifying that fraction as well: \[ a = \frac{1}{9} \] Now we have two values for \( a \): \( \frac{2}{3} \) and \( \frac{1}{9} \). Since the two equations provide different results, there is an inconsistency. To clarify, the solution for \( a \) from the first equation is \( \frac{2}{3} \), while the second equation gives \( \frac{1}{9} \). Make sure to choose the correct equation consistent with the context of the problem.