14. \( 14 \frac{1}{6}-11 \frac{7}{8} \)

To tackle the subtraction \( 14 \frac{1}{6} - 11 \frac{7}{8} \), first convert both mixed numbers to improper fractions. For \( 14 \frac{1}{6} \), multiply \( 14 \) by \( 6 \) and add \( 1 \): \[ 14 \times 6 + 1 = 84 + 1 = 85 \] So, \( 14 \frac{1}{6} = \frac{85}{6} \). For \( 11 \frac{7}{8} \), multiply \( 11 \) by \( 8 \) and add \( 7 \): \[ 11 \times 8 + 7 = 88 + 7 = 95 \] So, \( 11 \frac{7}{8} = \frac{95}{8} \). Next, we need a common denominator to perform the subtraction. The least common multiple of \( 6 \) and \( 8 \) is \( 24 \). Now, convert both improper fractions: \[ \frac{85}{6} = \frac{85 \times 4}{6 \times 4} = \frac{340}{24} \] \[ \frac{95}{8} = \frac{95 \times 3}{8 \times 3} = \frac{285}{24} \] Now subtract: \[ \frac{340}{24} - \frac{285}{24} = \frac{340 - 285}{24} = \frac{55}{24} \] Finally, convert back to a mixed number: \[ 55 \div 24 = 2 \text{ R } 7 \] Thus, \( \frac{55}{24} = 2 \frac{7}{24} \). So, the final result is \( 2 \frac{7}{24} \).