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\frac{1}{10}+\frac{4}{10}
Least common multiple of 10 and 5 is 10. Convert \frac{1}{10} and \frac{2}{5} to fractions with denominator 10.
\frac{1+4}{10}
Since \frac{1}{10} and \frac{4}{10} have the same denominator, add them by adding their numerators.
\frac{5}{10}
Add 1 and 4 to get 5.
\frac{1}{2}
Reduce the fraction \frac{5}{10} to lowest terms by extracting and canceling out 5.