Question

11/8 ×[( -5/11 : 13/8 - 5/11 : 13/5)+ -6/33]+ -3/4

Answer 1

\(\dfrac{11}{8}\cdot\left[-\dfrac{5}{11}:\dfrac{13}{8}-\dfrac{5}{11}:\dfrac{13}{5}+\dfrac{-6}{33}\right]+\dfrac{-3}{4}\)

\(=\dfrac{11}{8}\cdot\left[-\dfrac{5}{11}\left(\dfrac{8}{13}+\dfrac{5}{13}\right)+\dfrac{-2}{11}\right]+\dfrac{-3}{4}\)

\(=\dfrac{11}{8}\left(-\dfrac{5}{11}-\dfrac{2}{11}\right)+\dfrac{-3}{4}=\dfrac{-7}{8}+\dfrac{-6}{8}=-\dfrac{13}{8}\)

Answer 2

\(\dfrac{11}{8}.\left[\left(\dfrac{-5}{11}:\dfrac{13}{8}-\dfrac{5}{11}:\dfrac{13}{5}\right)+\dfrac{-6}{33}\right]+\dfrac{-3}{4}\)
\(=\dfrac{11}{8}.\left[\left(\dfrac{5}{11}.\dfrac{-8}{13}-\dfrac{5}{11}.\dfrac{5}{13}\right)-\dfrac{6}{33}\right]-\dfrac{3}{4}\)
\(=\dfrac{11}{8}.\left[\left(\dfrac{5}{11}.\left(\dfrac{-8}{13}-\dfrac{5}{13}\right)\right)-\dfrac{6}{33}\right]-\dfrac{3}{4}\)
\(=\dfrac{11}{8}.\left[\left(\dfrac{5}{11}.\left(-1\right)\right)-\dfrac{6}{33}\right]-\dfrac{3}{4}\)
\(=\dfrac{11}{8}.\left[\dfrac{-5}{11}-\dfrac{6}{33}\right]-\dfrac{3}{4}\)
\(=\dfrac{11}{8}.\left[\dfrac{-15}{33}-\dfrac{6}{33}\right]-\dfrac{3}{4}\)
\(=\dfrac{11}{8}.\dfrac{-21}{33}-\dfrac{3}{4}\)
\(=\dfrac{11}{8}.\dfrac{-7}{11}-\dfrac{3}{4}\)
\(=\dfrac{-7}{8}-\dfrac{3}{4}\)
\(=\dfrac{-7}{8}-\dfrac{6}{8}\)
\(=\dfrac{-13}{8}\)

Answer 3