Question

\((\dfrac{13}{30}+\dfrac{5}{11})-(3\dfrac{1}{2}+\dfrac{5}{11}-\dfrac{17}{30})\)

Answer 1

\(\left(\dfrac{13}{30}+\dfrac{5}{11}\right)-\left(3\dfrac{1}{2}+\dfrac{5}{11}-\dfrac{17}{30}\right)\)

\(=\left(\dfrac{13}{30}+\dfrac{5}{11}\right)-\left(\dfrac{7}{2}+\dfrac{5}{11}-\dfrac{17}{30}\right)\)

\(=\dfrac{13}{30}+\dfrac{5}{11}-\dfrac{7}{2}+\dfrac{5}{11}-\dfrac{17}{30}\)

\(=\left(\dfrac{13}{30}+\dfrac{17}{30}\right)-\dfrac{5}{11}-\dfrac{7}{2}+\dfrac{5}{11}\)

\(=1-\dfrac{5}{11}-\dfrac{7}{2}+\dfrac{5}{11}\)

\(=\left(1-\dfrac{5}{11}\right)-\dfrac{7}{2}+\dfrac{5}{11}\)

\(=\dfrac{6}{11}-\dfrac{7}{2}+\dfrac{5}{11}\)

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

\(=1-\dfrac{7}{2}\)

\(=-\dfrac{5}{2}\)