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\frac{50+3}{10}-\frac{3\times 15+8}{15}
Multiply 5 and 10 to get 50.
\frac{53}{10}-\frac{3\times 15+8}{15}
Add 50 and 3 to get 53.
\frac{53}{10}-\frac{45+8}{15}
Multiply 3 and 15 to get 45.
\frac{53}{10}-\frac{53}{15}
Add 45 and 8 to get 53.
\frac{159}{30}-\frac{106}{30}
Least common multiple of 10 and 15 is 30. Convert \frac{53}{10} and \frac{53}{15} to fractions with denominator 30.
\frac{159-106}{30}
Since \frac{159}{30} and \frac{106}{30} have the same denominator, subtract them by subtracting their numerators.
\frac{53}{30}
Subtract 106 from 159 to get 53.