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\frac{4}{40}+\frac{15}{40}
Least common multiple of 10 and 8 is 40. Convert \frac{1}{10} and \frac{3}{8} to fractions with denominator 40.
\frac{4+15}{40}
Since \frac{4}{40} and \frac{15}{40} have the same denominator, add them by adding their numerators.
\frac{19}{40}
Add 4 and 15 to get 19.