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\frac{5}{10}+\frac{8}{10}
Least common multiple of 2 and 5 is 10. Convert \frac{1}{2} and \frac{4}{5} to fractions with denominator 10.
\frac{5+8}{10}
Since \frac{5}{10} and \frac{8}{10} have the same denominator, add them by adding their numerators.
\frac{13}{10}
Add 5 and 8 to get 13.