Which expression is equivalent to \( -4 \frac{1}{5}+5 \frac{1}{6} \) ?

To solve the expression \( -4 \frac{1}{5} + 5 \frac{1}{6} \), we first convert the mixed numbers into improper fractions. For \( -4 \frac{1}{5} \): \[ -4 \frac{1}{5} = -\left(4 \times 5 + 1\right)/5 = -\frac{21}{5} \] For \( 5 \frac{1}{6} \): \[ 5 \frac{1}{6} = (5 \times 6 + 1)/6 = \frac{31}{6} \] Now we can add these two fractions together. We need a common denominator, which for 5 and 6 is 30. Converting the fractions: \[ -\frac{21}{5} = -\frac{21 \times 6}{5 \times 6} = -\frac{126}{30} \] \[ \frac{31}{6} = \frac{31 \times 5}{6 \times 5} = \frac{155}{30} \] Now we can combine them: \[ -\frac{126}{30} + \frac{155}{30} = \frac{155 - 126}{30} = \frac{29}{30} \] So, the expression \( -4 \frac{1}{5} + 5 \frac{1}{6} \) is equivalent to \( \frac{29}{30} \).