8. \( \frac{3}{4}-2 \frac{5}{6}-1 \frac{3}{8} \)

To solve the expression \( \frac{3}{4} - 2 \frac{5}{6} - 1 \frac{3}{8} \), we first convert the mixed numbers into improper fractions. 1. Convert \( 2 \frac{5}{6} \): \[ 2 \frac{5}{6} = 2 \times 6 + 5 = 12 + 5 = 17 \quad \Rightarrow \quad \frac{17}{6} \] 2. Convert \( 1 \frac{3}{8} \): \[ 1 \frac{3}{8} = 1 \times 8 + 3 = 8 + 3 = 11 \quad \Rightarrow \quad \frac{11}{8} \] Now, we rewrite the expression: \[ \frac{3}{4} - \frac{17}{6} - \frac{11}{8} \] Next, we need a common denominator to combine these fractions. The denominators are 4, 6, and 8. The least common multiple (LCM) of these numbers is 24. Now, we convert each fraction to have a denominator of 24: 1. Convert \( \frac{3}{4} \): \[ \frac{3}{4} = \frac{3 \times 6}{4 \times 6} = \frac{18}{24} \] 2. Convert \( \frac{17}{6} \): \[ \frac{17}{6} = \frac{17 \times 4}{6 \times 4} = \frac{68}{24} \] 3. Convert \( \frac{11}{8} \): \[ \frac{11}{8} = \frac{11 \times 3}{8 \times 3} = \frac{33}{24} \] Now we can rewrite the expression with a common denominator: \[ \frac{18}{24} - \frac{68}{24} - \frac{33}{24} \] Combine the fractions: \[ \frac{18 - 68 - 33}{24} = \frac{18 - 101}{24} = \frac{-83}{24} \] Thus, the final result is: \[ \boxed{-\frac{83}{24}} \]