8 5/9+12 7/9 -20 1/9

To solve the expression \( 8 \frac{5}{9} + 12 \frac{7}{9} - 20 \frac{1}{9} \), we can first convert the mixed numbers into improper fractions. 1. Convert \( 8 \frac{5}{9} \): \[ 8 \frac{5}{9} = \frac{8 \times 9 + 5}{9} = \frac{72 + 5}{9} = \frac{77}{9} \] 2. Convert \( 12 \frac{7}{9} \): \[ 12 \frac{7}{9} = \frac{12 \times 9 + 7}{9} = \frac{108 + 7}{9} = \frac{115}{9} \] 3. Convert \( 20 \frac{1}{9} \): \[ 20 \frac{1}{9} = \frac{20 \times 9 + 1}{9} = \frac{180 + 1}{9} = \frac{181}{9} \] Now, substitute these improper fractions back into the expression: \[ \frac{77}{9} + \frac{115}{9} - \frac{181}{9} \] Since all fractions have the same denominator, we can combine them: \[ \frac{77 + 115 - 181}{9} \] Calculating the numerator: \[ 77 + 115 = 192 \] \[ 192 - 181 = 11 \] So, we have: \[ \frac{11}{9} \] This is an improper fraction, which can be converted back to a mixed number: \[ 1 \frac{2}{9} \] Thus, the final result of \( 8 \frac{5}{9} + 12 \frac{7}{9} - 20 \frac{1}{9} \) is: \[ 1 \frac{2}{9} \]