Calculate the following: \( \begin{array}{ll}\text { a. } 5 \frac{1}{3}+1 \frac{2}{4} & \text { b. } 4 \frac{3}{8}-3 \frac{4}{6}\end{array} \)

Let's break down each calculation step by step! For the first calculation, \( 5 \frac{1}{3} + 1 \frac{2}{4} \): 1. Begin by converting the mixed numbers to improper fractions. \( 5 \frac{1}{3} = \frac{16}{3} \) and \( 1 \frac{2}{4} = 1 \frac{1}{2} = \frac{3}{2} \). 2. To add these, find a common denominator, which is 6. Convert them: \( \frac{16}{3} = \frac{32}{6} \) and \( \frac{3}{2} = \frac{9}{6} \). 3. Now add: \( \frac{32}{6} + \frac{9}{6} = \frac{41}{6} \). 4. This improper fraction can also be expressed as a mixed number: \( 6 \frac{5}{6} \). For the second calculation, \( 4 \frac{3}{8} - 3 \frac{4}{6} \): 1. First, convert to improper fractions again. \( 4 \frac{3}{8} = \frac{35}{8} \) and \( 3 \frac{4}{6} = 3 \frac{2}{3} = \frac{11}{3} \). 2. Find a common denominator for \( \frac{35}{8} - \frac{11}{3} \). The least common multiple is 24. Convert them: \( \frac{35}{8} = \frac{105}{24} \) and \( \frac{11}{3} = \frac{88}{24} \). 3. Subtract: \( \frac{105}{24} - \frac{88}{24} = \frac{17}{24} \). 4. Since \( \frac{17}{24} \) is already a proper fraction, there's no need to convert it further. So, the results are: a. \( 5 \frac{1}{3} + 1 \frac{2}{4} = 6 \frac{5}{6} \) b. \( 4 \frac{3}{8} - 3 \frac{4}{6} = \frac{17}{24} \)