4. \( 4 \frac{1}{3}+1 \frac{1}{13}= \)

To solve \( 4 \frac{1}{3}+1 \frac{1}{13} \), we first convert the mixed numbers into improper fractions. \( 4 \frac{1}{3} = \frac{13}{3} \) and \( 1 \frac{1}{13} = \frac{14}{13} \). Now we need a common denominator to add these fractions. The least common multiple of 3 and 13 is 39. Converting both fractions: \( \frac{13}{3} \) becomes \( \frac{13 \times 13}{3 \times 13} = \frac{169}{39} \) and \( \frac{14}{13} \) becomes \( \frac{14 \times 3}{13 \times 3} = \frac{42}{39} \). Now we can add: \[ \frac{169}{39} + \frac{42}{39} = \frac{211}{39}. \] Thus, \( 4 \frac{1}{3} + 1 \frac{1}{13} = \frac{211}{39} \), which can also be expressed as \( 5 \frac{16}{39} \) if you convert it back to a mixed number. Now, wasn't that a fun math adventure? Who knew fractions and mixed numbers could be this exciting? Just remember to always find that common denominator!