Find the sum by converting the mixed numbers to improper fractions: 559+379.

Calculation:
Given ${\displaystyle 5\frac{5}{9}+3\frac{7}{9}}$
Writing the mixed numbers as improper functions,
${\displaystyle 5\frac{5}{9}+3\frac{7}{9}=\frac{9\left(5\right)+5}{9}+\frac{9\left(3\right)+5}{9}}$
${\displaystyle 5\frac{5}{9}+3\frac{7}{9}=\frac{45+5}{9}+\frac{27+5}{9}}$
${\displaystyle 5\frac{5}{9}+3\frac{7}{9}=\frac{50}{9}+\frac{32}{9}}$
To add or subtract rational numbers the denominators need to be equal.
When the denominators are equal, the numerators can be added or subtracted as per the operation.
Hence, ${\displaystyle 5\frac{5}{9}+3\frac{7}{9}=\frac{50+32}{9}}$
${\displaystyle 5\frac{5}{9}+3\frac{7}{9}=\frac{82}{9}}$
To convert the improper fraction to mixed fraction, the numerator is written as sum of a multiple of denominator and the remainder.
${\displaystyle 5\frac{5}{9}+3\frac{7}{9}=\frac{81+1}{9}}$
${\displaystyle 5\frac{5}{9}+3\frac{7}{9}=\frac{81}{9}+\frac{1}{9}}$
${\displaystyle 5\frac{5}{9}+3\frac{7}{9}=9+\frac{1}{9}}$
${\displaystyle 5\frac{5}{9}+3\frac{7}{9}=9\frac{1}{9}}$
Therefore, ${\displaystyle 5\frac{5}{9}+3\frac{7}{9}=9\frac{1}{9}}$.