Problem
$\frac{1}{\frac{1}{9}+\frac{1}{27}+\frac{1}{18}}$
Solution
Step 1 ：Given the expression \(\frac{1}{\frac{1}{9}+\frac{1}{27}+\frac{1}{18}}\), we are asked to find the reciprocal of the sum of three fractions.
Step 2 ：First, we calculate the sum of the three fractions: \(\frac{1}{9}+\frac{1}{27}+\frac{1}{18} = 0.2037037037037037\).
Step 3 ：Next, we take the reciprocal of this sum: \(\frac{1}{0.2037037037037037} = 4.909090909090909\).
Step 4 ：Thus, the solution to the given expression is \(\boxed{4.909090909090909}\).
