Calculate the following sums and differences without converting to improper fractions. Give your answer as a mixed number. \( \begin{array}{lll}\text { a } 5 \frac{7}{8}-4 \frac{3}{8} & \text { b } 5 \frac{3}{8}-4 \frac{7}{8} & \text { e } 4 \frac{7}{8}-5 \frac{3}{8} \\ \text { d } 4 \frac{3}{8}-5 \frac{7}{8} & \text { e } 5 \frac{7}{8}+4 \frac{3}{8} & \text { f }-5 \frac{7}{8}+\left(-4 \frac{3}{8}\right)\end{array} \)

Let's solve each of the sums and differences step by step without converting to improper fractions, and we will express the final answers as mixed numbers. ### a) \( 5 \frac{7}{8} - 4 \frac{3}{8} \) 1. Subtract the whole numbers: \( 5 - 4 = 1 \) 2. Subtract the fractions: \( \frac{7}{8} - \frac{3}{8} = \frac{4}{8} = \frac{1}{2} \) 3. Combine the results: \( 1 + \frac{1}{2} = 1 \frac{1}{2} \) **Answer: \( 1 \frac{1}{2} \)** ### b) \( 5 \frac{3}{8} - 4 \frac{7}{8} \) 1. Subtract the whole numbers: \( 5 - 4 = 1 \) 2. Subtract the fractions: \( \frac{3}{8} - \frac{7}{8} = -\frac{4}{8} = -\frac{1}{2} \) 3. Combine the results: \( 1 - \frac{1}{2} = \frac{1}{2} \) **Answer: \( \frac{1}{2} \)** ### c) \( 4 \frac{7}{8} - 5 \frac{3}{8} \) 1. Subtract the whole numbers: \( 4 - 5 = -1 \) 2. Subtract the fractions: \( \frac{7}{8} - \frac{3}{8} = \frac{4}{8} = \frac{1}{2} \) 3. Combine the results: \( -1 + \frac{1}{2} = -\frac{2}{2} + \frac{1}{2} = -\frac{1}{2} \) **Answer: \( -\frac{1}{2} \)** ### d) \( 4 \frac{3}{8} - 5 \frac{7}{8} \) 1. Subtract the whole numbers: \( 4 - 5 = -1 \) 2. Subtract the fractions: \( \frac{3}{8} - \frac{7}{8} = -\frac{4}{8} = -\frac{1}{2} \) 3. Combine the results: \( -1 - \frac{1}{2} = -\frac{2}{2} - \frac{1}{2} = -\frac{3}{2} = -1 \frac{1}{2} \) **Answer: \( -1 \frac{1}{2} \)** ### e) \( 5 \frac{7}{8} + 4 \frac{3}{8} \) 1. Add the whole numbers: \( 5 + 4 = 9 \) 2. Add the fractions: \( \frac{7}{8} + \frac{3}{8} = \frac{10}{8} = 1 \frac{2}{8} = 1 \frac{1}{4} \) 3. Combine the results: \( 9 + 1 \frac{1}{4} = 10 \frac{1}{4} \) **Answer: \( 10 \frac{1}{4} \)** ### f) \( -5 \frac{7}{8} + (-4 \frac{3}{8}) \) 1. Convert to positive: \( -5 \frac{7}{8} - 4 \frac{3}{8} \) 2. Add the whole numbers: \( -5 - 4 = -9 \) 3. Add the fractions: \( -\frac{7}{8} - \frac{3}{8} = -\frac{10}{8} = -1 \frac{2}{8} = -1 \frac{1}{4} \) 4. Combine the results: \( -9 - 1 \frac{1}{4} = -10 \frac{1}{4} \) **Answer: \( -10 \frac{1}{4} \)** ### Summary of Answers: - a) \( 1 \frac{1}{2} \) - b) \( \frac{1}{2} \) - c) \( -\frac{1}{2} \) - d) \( -1 \frac{1}{2} \) - e) \( 10 \frac{1}{4} \) - f) \( -10 \frac{1}{4} \)