Which expression is equivalent to \( -4 \frac{1}{6}+2 \frac{2}{3} \) ?

To find the expression equivalent to \( -4 \frac{1}{6}+2 \frac{2}{3} \), we first convert the mixed numbers to improper fractions. For \( -4 \frac{1}{6} \): \[ -4 \frac{1}{6} = -\left(4 \times 6 + 1\right)/6 = -\frac{25}{6} \] For \( 2 \frac{2}{3} \): \[ 2 \frac{2}{3} = \left(2 \times 3 + 2\right)/3 = \frac{8}{3} \] Now we can add the two fractions: \[ -\frac{25}{6} + \frac{8}{3} \] To add these, we need a common denominator. The least common multiple of 6 and 3 is 6. We convert \( \frac{8}{3} \) to sixths: \[ \frac{8}{3} = \frac{8 \times 2}{3 \times 2} = \frac{16}{6} \] Now we can add: \[ -\frac{25}{6} + \frac{16}{6} = \frac{-25 + 16}{6} = \frac{-9}{6} \] This simplifies to: \[ \frac{-3}{2} \] Thus, the expression equivalent to \( -4 \frac{1}{6} + 2 \frac{2}{3} \) is \( -\frac{3}{2} \).