Work out these additions and subtractions. Show all the steps in your working. \( \begin{array}{lllll}\text { (d) } 2 \frac{2}{3}+\frac{5}{6} & \text { b. } 5 \frac{5}{6}-\frac{11}{12} & \text { (c) } 1 \frac{1}{8}+1 \frac{7}{24} & \text { (d) } 4 \frac{3}{4}-1 \frac{15}{16} & \text { el } 5 \frac{5}{32}+1\end{array} \)

Sure! Let’s work through each of these additions and subtractions step by step. **(a)** \( 2 \frac{2}{3} + \frac{5}{6} \) 1. Convert \( 2 \frac{2}{3} \) to an improper fraction: \( 2 \frac{2}{3} = 2 \times 3 + 2 = 6 + 2 = \frac{8}{3} \). 2. Find a common denominator for \( \frac{8}{3} \) and \( \frac{5}{6} \): The least common denominator (LCD) is 6. Convert \( \frac{8}{3} \) to sixths: \( \frac{8}{3} = \frac{8 \times 2}{3 \times 2} = \frac{16}{6} \). 3. Add the fractions: \( \frac{16}{6} + \frac{5}{6} = \frac{16 + 5}{6} = \frac{21}{6} \). 4. Convert to a mixed number: \( \frac{21}{6} = 3 \frac{3}{6} = 3 \frac{1}{2} \). Thus, \( 2 \frac{2}{3} + \frac{5}{6} = 3 \frac{1}{2} \). --- **(b)** \( 5 \frac{5}{6} - \frac{11}{12} \) 1. Convert \( 5 \frac{5}{6} \) to an improper fraction: \( 5 \frac{5}{6} = 5 \times 6 + 5 = 30 + 5 = \frac{35}{6} \). 2. Find a common denominator for \( \frac{35}{6} \) and \( \frac{11}{12} \): The LCD is 12. Convert \( \frac{35}{6} \) to twelfths: \( \frac{35}{6} = \frac{35 \times 2}{6 \times 2} = \frac{70}{12} \). 3. Subtract the fractions: \( \frac{70}{12} - \frac{11}{12} = \frac{70 - 11}{12} = \frac{59}{12} \). 4. Convert to a mixed number: \( \frac{59}{12} = 4 \frac{11}{12} \). Thus, \( 5 \frac{5}{6} - \frac{11}{12} = 4 \frac{11}{12} \). --- **(c)** \( 1 \frac{1}{8} + 1 \frac{7}{24} \) 1. Convert both mixed numbers to improper fractions: \( 1 \frac{1}{8} = \frac{8 + 1}{8} = \frac{9}{8} \) and \( 1 \frac{7}{24} = \frac{24 + 7}{24} = \frac{31}{24} \). 2. Find a common denominator for \( \frac{9}{8} \) and \( \frac{31}{24} \): The LCD is 24. Convert \( \frac{9}{8} \) to twenty-fourths: \( \frac{9}{8} = \frac{9 \times 3}{8 \times 3} = \frac{27}{24} \). 3. Add the fractions: \( \frac{27}{24} + \frac{31}{24} = \frac{27 + 31}{24} = \frac{58}{24} \). 4. Convert to a mixed number: \( \frac{58}{24} = 2 \frac{10}{24} = 2 \frac{5}{12} \). Thus, \( 1 \frac{1}{8} + 1 \frac{7}{24} = 2 \frac{5}{12} \). --- **(d)** \( 4 \frac{3}{4} - 1 \frac{15}{16} \) 1. Convert both mixed numbers to improper fractions: \( 4 \frac{3}{4} = \frac{16 + 3}{4} = \frac{19}{4} \) and \( 1 \frac{15