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\frac{1}{2}\times \frac{9}{4}\times \left(\frac{2}{15}\right)^{2}+4.5\times \frac{2}{15}
Convert decimal number 2.25 to fraction \frac{225}{100}. Reduce the fraction \frac{225}{100} to lowest terms by extracting and canceling out 25.
\frac{1\times 9}{2\times 4}\times \left(\frac{2}{15}\right)^{2}+4.5\times \frac{2}{15}
Multiply \frac{1}{2} times \frac{9}{4} by multiplying numerator times numerator and denominator times denominator.
\frac{9}{8}\times \left(\frac{2}{15}\right)^{2}+4.5\times \frac{2}{15}
Do the multiplications in the fraction \frac{1\times 9}{2\times 4}.
\frac{9}{8}\times \frac{4}{225}+4.5\times \frac{2}{15}
Calculate \frac{2}{15} to the power of 2 and get \frac{4}{225}.
\frac{9\times 4}{8\times 225}+4.5\times \frac{2}{15}
Multiply \frac{9}{8} times \frac{4}{225} by multiplying numerator times numerator and denominator times denominator.
\frac{36}{1800}+4.5\times \frac{2}{15}
Do the multiplications in the fraction \frac{9\times 4}{8\times 225}.
\frac{1}{50}+4.5\times \frac{2}{15}
Reduce the fraction \frac{36}{1800} to lowest terms by extracting and canceling out 36.
\frac{1}{50}+\frac{9}{2}\times \frac{2}{15}
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{1}{50}+\frac{9\times 2}{2\times 15}
Multiply \frac{9}{2} times \frac{2}{15} by multiplying numerator times numerator and denominator times denominator.
\frac{1}{50}+\frac{9}{15}
Cancel out 2 in both numerator and denominator.
\frac{1}{50}+\frac{3}{5}
Reduce the fraction \frac{9}{15} to lowest terms by extracting and canceling out 3.
\frac{1}{50}+\frac{30}{50}
Least common multiple of 50 and 5 is 50. Convert \frac{1}{50} and \frac{3}{5} to fractions with denominator 50.
\frac{1+30}{50}
Since \frac{1}{50} and \frac{30}{50} have the same denominator, add them by adding their numerators.
\frac{31}{50}
Add 1 and 30 to get 31.