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\frac{82}{2870}+\frac{35}{2870}
Least common multiple of 35 and 82 is 2870. Convert \frac{1}{35} and \frac{1}{82} to fractions with denominator 2870.
\frac{82+35}{2870}
Since \frac{82}{2870} and \frac{35}{2870} have the same denominator, add them by adding their numerators.
\frac{117}{2870}
Add 82 and 35 to get 117.