Math Problem Solver

\[ 27 - \frac{18}{-189} + 45 = \frac{1514}{21} = 72.\overline{095238} \]

The sum can be computed by rewriting each term over a common denominator, where the least common denominator of \(\frac{27}{1}\), \(\frac{-18}{-189}\), and \(\frac{45}{1}\) is \(189\). \[ \begin{aligned} 27 - \frac{18}{-189} + 45 &= \frac{27 \cdot 189}{1 \cdot 189} + \frac{-18 \cdot -1}{-189 \cdot -1} + \frac{45 \cdot 189}{1 \cdot 189} \\ &= \frac{5103 + 18 + 8505}{189} \\ &= \frac{13626}{189} \\&= \frac{1514}{21} \end{aligned} \]