puntgewelb5

2021-11-17

Find the sum by converting the mixed numbers to improper fractions: $5\frac{5}{9}+3\frac{7}{9}$.

Kathleen Ashton

Calculation:
Given $5\frac{5}{9}+3\frac{7}{9}$
Writing the mixed numbers as improper functions,
$5\frac{5}{9}+3\frac{7}{9}=\frac{9\left(5\right)+5}{9}+\frac{9\left(3\right)+5}{9}$
$5\frac{5}{9}+3\frac{7}{9}=\frac{45+5}{9}+\frac{27+5}{9}$
$5\frac{5}{9}+3\frac{7}{9}=\frac{50}{9}+\frac{32}{9}$
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, $5\frac{5}{9}+3\frac{7}{9}=\frac{50+32}{9}$
$5\frac{5}{9}+3\frac{7}{9}=\frac{82}{9}$
To convert the improper fraction to mixed fraction, the numerator is written as sum of a multiple of denominator and the remainder.
$5\frac{5}{9}+3\frac{7}{9}=\frac{81+1}{9}$
$5\frac{5}{9}+3\frac{7}{9}=\frac{81}{9}+\frac{1}{9}$
$5\frac{5}{9}+3\frac{7}{9}=9+\frac{1}{9}$
$5\frac{5}{9}+3\frac{7}{9}=9\frac{1}{9}$
Therefore, $5\frac{5}{9}+3\frac{7}{9}=9\frac{1}{9}$.

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