-2 5/9-(-1 20/21)

To solve the expression \(-2 \frac{5}{9} - (-1 \frac{20}{21})\), we first convert the mixed numbers to improper fractions. 1. Convert \(-2 \frac{5}{9}\) to an improper fraction: \[ -2 \frac{5}{9} = -\left(2 \times 9 + 5\right)/9 = -\frac{18 + 5}{9} = -\frac{23}{9} \] 2. Convert \(-1 \frac{20}{21}\) to an improper fraction: \[ -1 \frac{20}{21} = -\left(1 \times 21 + 20\right)/21 = -\frac{21 + 20}{21} = -\frac{41}{21} \] Next, substituting the values we get: \[ -\frac{23}{9} - (-\frac{41}{21}) = -\frac{23}{9} + \frac{41}{21} \] To add these two fractions, we need a common denominator. The least common multiple of 9 and 21 is 63. 3. Convert each fraction: - For \(-\frac{23}{9}\): \[ -\frac{23}{9} = -\frac{23 \times 7}{9 \times 7} = -\frac{161}{63} \] - For \(\frac{41}{21}\): \[ \frac{41}{21} = \frac{41 \times 3}{21 \times 3} = \frac{123}{63} \] Now we can add the two fractions: \[ -\frac{161}{63} + \frac{123}{63} = \frac{-161 + 123}{63} = \frac{-38}{63} \] Therefore, the final result is: \[ -2 \frac{5}{9} - (-1 \frac{20}{21}) = -\frac{38}{63} \]