13. \( 4 \frac{9}{100}+5 \frac{11}{100} \) 16. \( 2 \frac{1}{2}-\frac{2}{5} \) 19. \( 2 \frac{1}{3}+1 \frac{1}{2} \)

To combine mixed numbers like \( 4 \frac{9}{100} + 5 \frac{11}{100} \), you can first convert them into improper fractions. So, \( 4 \frac{9}{100} = \frac{409}{100} \) and \( 5 \frac{11}{100} = \frac{511}{100} \). Adding those gives you \( \frac{920}{100} \) which simplifies to \( 9 \frac{20}{100} \) or \( 9 \frac{1}{5} \). For \( 2 \frac{1}{2} - \frac{2}{5} \), convert \( 2 \frac{1}{2} \) to improper: \( 2 \frac{1}{2} = \frac{5}{2} \). Now you need a common denominator to subtract. The least common multiple of 2 and 5 is 10, so convert: \( \frac{5}{2} = \frac{25}{10} \) and \( \frac{2}{5} = \frac{4}{10} \). Subtracting gives you \( \frac{21}{10} \) or \( 2 \frac{1}{10} \). For \( 2 \frac{1}{3} + 1 \frac{1}{2} \), change to improper: \( 2 \frac{1}{3} = \frac{7}{3} \) and \( 1 \frac{1}{2} = \frac{3}{2} \). With a common denominator of 6, \( \frac{7}{3} = \frac{14}{6} \) and \( \frac{3}{2} = \frac{9}{6} \). Adding up gives \( \frac{23}{6} \) or \( 3 \frac{5}{6} \). Math can sometimes feel like a puzzle, but every piece fits perfectly when you use the right strategy!