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

Let's simplify each expression step by step. ### a. \( -\frac{3}{4} - \frac{2}{5} \) 1. **Find a common denominator:** The least common multiple (LCM) of 4 and 5 is 20. 2. **Convert each fraction to have the common denominator:** \[ -\frac{3}{4} = -\frac{3 \times 5}{4 \times 5} = -\frac{15}{20} \] \[ -\frac{2}{5} = -\frac{2 \times 4}{5 \times 4} = -\frac{8}{20} \] 3. **Subtract the fractions:** \[ -\frac{15}{20} - \frac{8}{20} = -\frac{23}{20} \] 4. **Simplify (if necessary):** \[ -\frac{23}{20} = -1 \frac{3}{20} \] **Final Answer for a:** \[ -\frac{23}{20} \quad \text{or} \quad -1 \frac{3}{20} \] --- ### b. \( \frac{1}{8} - \frac{2}{3} \) 1. **Find a common denominator:** The least common multiple (LCM) of 8 and 3 is 24. 2. **Convert each fraction to have the common denominator:** \[ \frac{1}{8} = \frac{1 \times 3}{8 \times 3} = \frac{3}{24} \] \[ \frac{2}{3} = \frac{2 \times 8}{3 \times 8} = \frac{16}{24} \] 3. **Subtract the fractions:** \[ \frac{3}{24} - \frac{16}{24} = -\frac{13}{24} \] 4. **Simplify (if necessary):** - The fraction \(-\frac{13}{24}\) is already in its simplest form. **Final Answer for b:** \[ -\frac{13}{24} \]