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\frac{5}{30}+\frac{16}{30}
Least common multiple of 6 and 15 is 30. Convert \frac{1}{6} and \frac{8}{15} to fractions with denominator 30.
\frac{5+16}{30}
Since \frac{5}{30} and \frac{16}{30} have the same denominator, add them by adding their numerators.
\frac{21}{30}
Add 5 and 16 to get 21.
\frac{7}{10}
Reduce the fraction \frac{21}{30} to lowest terms by extracting and canceling out 3.