e) \( 5 \frac{2}{9}-\frac{1}{3} \)

To solve \( 5 \frac{2}{9} - \frac{1}{3} \), start by converting the mixed number into an improper fraction. This gives us \( \frac{5 \times 9 + 2}{9} = \frac{47}{9} \). Next, we need to convert \( \frac{1}{3} \) into ninths for easier subtraction. Since \( \frac{1}{3} = \frac{3}{9} \), we can now perform the calculation: \[ \frac{47}{9} - \frac{3}{9} = \frac{44}{9} \] Now convert it back to a mixed number: \( 44 \div 9 = 4 \) remainder \( 8 \), giving us \( 4 \frac{8}{9} \). So, \( 5 \frac{2}{9}-\frac{1}{3} = 4 \frac{8}{9} \).