To find out how far Jessica walked altogether, we need to add the two distances she walked: \( \frac{1}{3} \) mile to the post office and \( \frac{2}{5} \) mile to the library.
First, we need a common denominator to add the fractions. The denominators are 3 and 5. The least common multiple of 3 and 5 is 15.
Next, we convert both fractions to have a denominator of 15:
- convert \( \frac{1}{3} \):
\[ \frac{1}{3} = \frac{1 \times 5}{3 \times 5} = \frac{5}{15} \]
- convert \( \frac{2}{5} \):
\[ \frac{2}{5} = \frac{2 \times 3}{5 \times 3} = \frac{6}{15} \]
Now we add the two fractions:
\[ \frac{5}{15} + \frac{6}{15} = \frac{5 + 6}{15} = \frac{11}{15} \]
Thus, the total distance Jessica walked is \( \frac{11}{15} \) miles.