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4.5+\frac{95}{20}
Expand \frac{9.5}{2} by multiplying both numerator and the denominator by 10.
4.5+\frac{19}{4}
Reduce the fraction \frac{95}{20} to lowest terms by extracting and canceling out 5.
\frac{9}{2}+\frac{19}{4}
Convert decimal number 4.5 to fraction \frac{45}{10}. Reduce the fraction \frac{45}{10} to lowest terms by extracting and canceling out 5.
\frac{18}{4}+\frac{19}{4}
Least common multiple of 2 and 4 is 4. Convert \frac{9}{2} and \frac{19}{4} to fractions with denominator 4.
\frac{18+19}{4}
Since \frac{18}{4} and \frac{19}{4} have the same denominator, add them by adding their numerators.
\frac{37}{4}
Add 18 and 19 to get 37.