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

To solve the expression \( -4 \frac{1}{5} + 5 \frac{1}{6} \), let's first convert the mixed numbers into improper fractions. Start with \( -4 \frac{1}{5} = -\frac{21}{5} \) (because \( 4 \times 5 + 1 = 21\)) and \( 5 \frac{1}{6} = \frac{31}{6} \) (since \( 5 \times 6 + 1 = 31\)). Now the expression becomes: \[ -\frac{21}{5} + \frac{31}{6} \] To add these fractions, we need a common denominator, which is 30. Convert both fractions: \[ -\frac{21}{5} = -\frac{126}{30} \quad \text{and} \quad \frac{31}{6} = \frac{155}{30} \] Now, add them: \[ -\frac{126}{30} + \frac{155}{30} = \frac{29}{30} \] Thus, the equivalent expression is \( \frac{29}{30} \).