(12.6) + (−7.4) + (22.6) + (22.6) + (42.6) + (−37.4) + (−15.4) + (14.6) + (−34.4) + (−20.4) =

asked by guest
on Oct 20, 2024 at 2:29 pm



You asked:

Evaluate the expression: \(12.6 + -7.4 + 22.6 + 22.6 + 42.6 + -37.4 + -15.4 + 14.6 + -34.4 + -20.4\)

MathBot Answer:

\[12.6 + -7.4 + 22.6 + 22.6 + 42.6 + -37.4 + -15.4 + 14.6 + -34.4 + -20.4 = 0\]

\[\begin{aligned}12.6 + -7.4 + 22.6 + 22.6 + 42.6 + -37.4 + -15.4 + 14.6 + -34.4 + -20.4& = 12 + \frac{6}{10} - \left(7 + \frac{4}{10}\right) + 22 + \frac{6}{10} + 22 + \frac{6}{10} + 42 + \frac{6}{10} - \left(37 + \frac{4}{10}\right) - \left(15 + \frac{4}{10}\right) + 14 + \frac{6}{10} - \left(34 + \frac{4}{10}\right) - \left(20 + \frac{4}{10}\right)\\& = 12 + \frac{3}{5} - \left(7 + \frac{4}{10}\right) + 22 + \frac{6}{10} + 22 + \frac{6}{10} + 42 + \frac{6}{10} - \left(37 + \frac{4}{10}\right) - \left(15 + \frac{4}{10}\right) + 14 + \frac{6}{10} - \left(34 + \frac{4}{10}\right) - \left(20 + \frac{4}{10}\right)\\& = 12 + \frac{3}{5} - \left(7 + \frac{2}{5}\right) + 22 + \frac{6}{10} + 22 + \frac{6}{10} + 42 + \frac{6}{10} - \left(37 + \frac{4}{10}\right) - \left(15 + \frac{4}{10}\right) + 14 + \frac{6}{10} - \left(34 + \frac{4}{10}\right) - \left(20 + \frac{4}{10}\right)\\& = 12 + \frac{3}{5} - \frac{37}{5} + 22 + \frac{6}{10} + 22 + \frac{6}{10} + 42 + \frac{6}{10} - \left(37 + \frac{4}{10}\right) - \left(15 + \frac{4}{10}\right) + 14 + \frac{6}{10} - \left(34 + \frac{4}{10}\right) - \left(20 + \frac{4}{10}\right)\\& = 12 + \frac{3}{5} - \frac{37}{5} + 22 + \frac{3}{5} + 22 + \frac{6}{10} + 42 + \frac{6}{10} - \left(37 + \frac{4}{10}\right) - \left(15 + \frac{4}{10}\right) + 14 + \frac{6}{10} - \left(34 + \frac{4}{10}\right) - \left(20 + \frac{4}{10}\right)\\& = 12 + \frac{3}{5} - \frac{37}{5} + 22 + \frac{3}{5} + 22 + \frac{3}{5} + 42 + \frac{6}{10} - \left(37 + \frac{4}{10}\right) - \left(15 + \frac{4}{10}\right) + 14 + \frac{6}{10} - \left(34 + \frac{4}{10}\right) - \left(20 + \frac{4}{10}\right)\\& = 12 + \frac{3}{5} - \frac{37}{5} + 22 + \frac{3}{5} + 22 + \frac{3}{5} + 42 + \frac{3}{5} - \left(37 + \frac{4}{10}\right) - \left(15 + \frac{4}{10}\right) + 14 + \frac{6}{10} - \left(34 + \frac{4}{10}\right) - \left(20 + \frac{4}{10}\right)\\& = 12 + \frac{3}{5} - \frac{37}{5} + 22 + \frac{3}{5} + 22 + \frac{3}{5} + 42 + \frac{3}{5} - \left(37 + \frac{2}{5}\right) - \left(15 + \frac{4}{10}\right) + 14 + \frac{6}{10} - \left(34 + \frac{4}{10}\right) - \left(20 + \frac{4}{10}\right)\\& = 12 + \frac{3}{5} - \frac{37}{5} + 22 + \frac{3}{5} + 22 + \frac{3}{5} + 42 + \frac{3}{5} - \frac{187}{5} - \left(15 + \frac{4}{10}\right) + 14 + \frac{6}{10} - \left(34 + \frac{4}{10}\right) - \left(20 + \frac{4}{10}\right)\\& = 12 + \frac{3}{5} - \frac{37}{5} + 22 + \frac{3}{5} + 22 + \frac{3}{5} + 42 + \frac{3}{5} - \frac{187}{5} - \left(15 + \frac{2}{5}\right) + 14 + \frac{6}{10} - \left(34 + \frac{4}{10}\right) - \left(20 + \frac{4}{10}\right)\\& = 12 + \frac{3}{5} - \frac{37}{5} + 22 + \frac{3}{5} + 22 + \frac{3}{5} + 42 + \frac{3}{5} - \frac{187}{5} - \frac{77}{5} + 14 + \frac{6}{10} - \left(34 + \frac{4}{10}\right) - \left(20 + \frac{4}{10}\right)\\& = 12 + \frac{3}{5} - \frac{37}{5} + 22 + \frac{3}{5} + 22 + \frac{3}{5} + 42 + \frac{3}{5} - \frac{187}{5} - \frac{77}{5} + 14 + \frac{3}{5} - \left(34 + \frac{4}{10}\right) - \left(20 + \frac{4}{10}\right)\\& = 12 + \frac{3}{5} - \frac{37}{5} + 22 + \frac{3}{5} + 22 + \frac{3}{5} + 42 + \frac{3}{5} - \frac{187}{5} - \frac{77}{5} + 14 + \frac{3}{5} - \left(34 + \frac{2}{5}\right) - \left(20 + \frac{4}{10}\right)\\& = 12 + \frac{3}{5} - \frac{37}{5} + 22 + \frac{3}{5} + 22 + \frac{3}{5} + 42 + \frac{3}{5} - \frac{187}{5} - \frac{77}{5} + 14 + \frac{3}{5} - \frac{172}{5} - \left(20 + \frac{4}{10}\right)\\& = 12 + \frac{3}{5} - \frac{37}{5} + 22 + \frac{3}{5} + 22 + \frac{3}{5} + 42 + \frac{3}{5} - \frac{187}{5} - \frac{77}{5} + 14 + \frac{3}{5} - \frac{172}{5} - \left(20 + \frac{2}{5}\right)\\& = 12 + \frac{3}{5} - \frac{37}{5} + 22 + \frac{3}{5} + 22 + \frac{3}{5} + 42 + \frac{3}{5} - \frac{187}{5} - \frac{77}{5} + 14 + \frac{3}{5} - \frac{172}{5} - \frac{102}{5}\\& = \frac{63}{5} - \frac{37}{5} + 22 + \frac{3}{5} + 22 + \frac{3}{5} + 42 + \frac{3}{5} - \frac{187}{5} - \frac{77}{5} + 14 + \frac{3}{5} - \frac{172}{5} - \frac{102}{5}\\& = \frac{26}{5} + 22 + \frac{3}{5} + 22 + \frac{3}{5} + 42 + \frac{3}{5} - \frac{187}{5} - \frac{77}{5} + 14 + \frac{3}{5} - \frac{172}{5} - \frac{102}{5}\\& = \frac{136}{5} + \frac{3}{5} + 22 + \frac{3}{5} + 42 + \frac{3}{5} - \frac{187}{5} - \frac{77}{5} + 14 + \frac{3}{5} - \frac{172}{5} - \frac{102}{5}\\& = \frac{139}{5} + 22 + \frac{3}{5} + 42 + \frac{3}{5} - \frac{187}{5} - \frac{77}{5} + 14 + \frac{3}{5} - \frac{172}{5} - \frac{102}{5}\\& = \frac{249}{5} + \frac{3}{5} + 42 + \frac{3}{5} - \frac{187}{5} - \frac{77}{5} + 14 + \frac{3}{5} - \frac{172}{5} - \frac{102}{5}\\& = \frac{252}{5} + 42 + \frac{3}{5} - \frac{187}{5} - \frac{77}{5} + 14 + \frac{3}{5} - \frac{172}{5} - \frac{102}{5}\\& = \frac{462}{5} + \frac{3}{5} - \frac{187}{5} - \frac{77}{5} + 14 + \frac{3}{5} - \frac{172}{5} - \frac{102}{5}\\& = 93 - \frac{187}{5} - \frac{77}{5} + 14 + \frac{3}{5} - \frac{172}{5} - \frac{102}{5}\\& = \frac{278}{5} - \frac{77}{5} + 14 + \frac{3}{5} - \frac{172}{5} - \frac{102}{5}\\& = \frac{201}{5} + 14 + \frac{3}{5} - \frac{172}{5} - \frac{102}{5}\\& = \frac{271}{5} + \frac{3}{5} - \frac{172}{5} - \frac{102}{5}\\& = \frac{274}{5} - \frac{172}{5} - \frac{102}{5}\\& = \frac{102}{5} - \frac{102}{5}\\& = 0\end{aligned}\]

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