Math Problem Solver

\[ 0.07783604747446867237096329009108474 + 8 - 0.1656086116478056858956665746618824255319148936170212765957446808510638297872340 + 0.97295059343085840463704112613855925 - 17 + 7.783604747446867237096329009108474 = - \frac{165608611647805685895666574661882217765957446808510638297872340425531914893617}{500000000000000000000000000000000000000000000000000000000000000000000000000000} = -0.331217223295611371791333149323764435531914893617021276595744680851063829787234 \]

The sum can be computed by rewriting each term over a common denominator, where the least common denominator of \(\frac{7783604747446867237096329009108474}{100000000000000000000000000000000000}\), \(\frac{8}{1}\), \(\frac{-165608611647805685895666574661882425531914893617021276595744680851063829787234}{1000000000000000000000000000000000000000000000000000000000000000000000000000000}\), \(\frac{97295059343085840463704112613855925}{100000000000000000000000000000000000}\), \(\frac{-17}{1}\), \(\frac{7}{1}\), and \(\frac{783604747446867237096329009108474}{1000000000000000000000000000000000}\) is \(1000000000000000000000000000000000000000000000000000000000000000000000000000000\). \[ \begin{aligned} 0.07783604747446867237096329009108474 + 8 - 0.1656086116478056858956665746618824255319148936170212765957446808510638297872340 + 0.97295059343085840463704112613855925 - 17 + 7.783604747446867237096329009108474 &= \frac{7783604747446867237096329009108474 \cdot 10000000000000000000000000000000000000000000}{100000000000000000000000000000000000 \cdot 10000000000000000000000000000000000000000000} + \frac{8 \cdot 1000000000000000000000000000000000000000000000000000000000000000000000000000000}{1 \cdot 1000000000000000000000000000000000000000000000000000000000000000000000000000000} + \frac{-165608611647805685895666574661882425531914893617021276595744680851063829787234 \cdot 1}{1000000000000000000000000000000000000000000000000000000000000000000000000000000 \cdot 1} + \frac{97295059343085840463704112613855925 \cdot 10000000000000000000000000000000000000000000}{100000000000000000000000000000000000 \cdot 10000000000000000000000000000000000000000000} + \frac{-17 \cdot 1000000000000000000000000000000000000000000000000000000000000000000000000000000}{1 \cdot 1000000000000000000000000000000000000000000000000000000000000000000000000000000} + \frac{7 \cdot 1000000000000000000000000000000000000000000000000000000000000000000000000000000}{1 \cdot 1000000000000000000000000000000000000000000000000000000000000000000000000000000} + \frac{783604747446867237096329009108474 \cdot 1000000000000000000000000000000000000000000000}{1000000000000000000000000000000000 \cdot 1000000000000000000000000000000000000000000000} \\ &= \frac{77836047474468672370963290091084740000000000000000000000000000000000000000000 + 8000000000000000000000000000000000000000000000000000000000000000000000000000000 + -165608611647805685895666574661882425531914893617021276595744680851063829787234 + 972950593430858404637041126138559250000000000000000000000000000000000000000000 + -17000000000000000000000000000000000000000000000000000000000000000000000000000000 + 7000000000000000000000000000000000000000000000000000000000000000000000000000000 + 783604747446867237096329009108474000000000000000000000000000000000000000000000}{1000000000000000000000000000000000000000000000000000000000000000000000000000000} \\ &= \frac{-331217223295611371791333149323764435531914893617021276595744680851063829787234}{1000000000000000000000000000000000000000000000000000000000000000000000000000000} \\&= - \frac{165608611647805685895666574661882217765957446808510638297872340425531914893617}{500000000000000000000000000000000000000000000000000000000000000000000000000000} \end{aligned} \]