Jimmy says 3; – 2 is a 4 2 - 1 / 3 What is the actual difference? What did Jimmy do wrong?

Given:
[tex]3\frac{4}{9}-2\frac{5}{6}\text{ is }1\frac{1}{3}[/tex][tex]\begin{gathered} 3\frac{4}{9}-2\frac{5}{6}=\frac{31}{9}-\frac{17}{6} \\ 3\frac{4}{9}-2\frac{5}{6}=\frac{62-51}{18} \\ 3\frac{4}{9}-2\frac{5}{6}=\frac{11}{18} \end{gathered}[/tex][tex]\text{Actual difference is }\frac{11}{18}[/tex]Jimmy done the subtraction directly without changing the mixed fraction to improper fraction and didn't took the LCM.