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\frac{15}{10}+\frac{8}{10}+\frac{3}{10}
Least common multiple of 2 and 5 is 10. Convert \frac{3}{2} and \frac{4}{5} to fractions with denominator 10.
\frac{15+8}{10}+\frac{3}{10}
Since \frac{15}{10} and \frac{8}{10} have the same denominator, add them by adding their numerators.
\frac{23}{10}+\frac{3}{10}
Add 15 and 8 to get 23.
\frac{23+3}{10}
Since \frac{23}{10} and \frac{3}{10} have the same denominator, add them by adding their numerators.
\frac{26}{10}
Add 23 and 3 to get 26.
\frac{13}{5}
Reduce the fraction \frac{26}{10} to lowest terms by extracting and canceling out 2.