Enter the value of \( \frac{5}{6}+\left(-\frac{4}{9}\right)-(-2) \)

Let's evaluate the expression step by step: \[ \frac{5}{6} + \left(-\frac{4}{9}\right) - (-2) \] 1. **Simplify the expression:** \[ \frac{5}{6} - \frac{4}{9} + 2 \] 2. **Find a common denominator for the fractions.** The denominators are 6 and 9. The least common denominator (LCD) is 18. - Convert \(\frac{5}{6}\) to eighteenth: \[ \frac{5}{6} = \frac{5 \times 3}{6 \times 3} = \frac{15}{18} \] - Convert \(-\frac{4}{9}\) to eighteenth: \[ -\frac{4}{9} = -\frac{4 \times 2}{9 \times 2} = -\frac{8}{18} \] 3. **Combine the fractions:** \[ \frac{15}{18} - \frac{8}{18} = \frac{15 - 8}{18} = \frac{7}{18} \] 4. **Add the whole number:** \[ \frac{7}{18} + 2 = 2 + \frac{7}{18} = \frac{36}{18} + \frac{7}{18} = \frac{43}{18} \] 5. **Simplify (if desired):** \(\frac{43}{18}\) is an improper fraction. It can also be expressed as a mixed number: \[ \frac{43}{18} = 2\,\frac{7}{18} \] **Final Answer:** \(\frac{43}{18}\) or \(2\,\frac{7}{18}\)