a) \(\left(-1+\dfrac{45}{115}+\dfrac{17}{51}\right)+\left(\dfrac{-9}{23}+\dfrac{-1}{3}\right)\)
\(=\left(-1+\dfrac{9}{23}+\dfrac{1}{3}\right)+\left(\dfrac{-9}{23}+\dfrac{-1}{3}\right)\)
\(=-1+\left(\dfrac{9}{23}-\dfrac{9}{23}\right)+\left(\dfrac{1}{3}-\dfrac{1}{3}\right)\)
\(=-1\)
b) \(\dfrac{-13}{39}+\dfrac{12}{48}+\dfrac{1}{12}+\dfrac{3}{18}\)
\(=\left(\dfrac{-1}{3}+\dfrac{1}{4}+\dfrac{1}{12}\right)+\dfrac{1}{6}\)
\(=\left(\dfrac{-4}{12}+\dfrac{3}{12}+\dfrac{1}{12}\right)+\dfrac{1}{6}\)
\(=0+\dfrac{1}{6}\)
\(=\dfrac{1}{6}\)
c) \(\dfrac{13}{15}+\left(\dfrac{-4}{5}+\dfrac{7}{18}\right)+\dfrac{-5}{12}+\dfrac{1}{36}\)
\(=\dfrac{13}{15}+\dfrac{-4}{5}+\dfrac{7}{18}+\dfrac{-5}{12}+\dfrac{1}{36}\)
\(=\left(\dfrac{13}{15}+\dfrac{-4}{5}\right)+\left(\dfrac{7}{18}+\dfrac{1}{36}+\dfrac{-5}{12}\right)\)
\(=\dfrac{1}{15}+\left(\dfrac{5}{12}+\dfrac{-5}{12}\right)\)
\(=\dfrac{1}{15}+0\)
\(=\dfrac{1}{15}\)
