Question

a) 18/24 + 35/-21 - 1/2

b) -2/3 - 3/-4 + 5/-6

c) ( 3/4 + -7/2) . ( 10/11 + 2/22)

d) ( 7/3 - -7/2) : ( -25/6 . 1/5)

Answer 1

a: \(\dfrac{18}{24}+\dfrac{35}{-21}-\dfrac{1}{2}\)

\(=\dfrac{3}{4}-\dfrac{5}{3}-\dfrac{1}{2}\)

\(=\dfrac{9-20-6}{12}=\dfrac{-17}{12}\)

b: \(\dfrac{-2}{3}-\dfrac{3}{-4}+\dfrac{5}{-6}\)

\(=-\dfrac{2}{3}+\dfrac{3}{4}-\dfrac{5}{6}\)

\(=\dfrac{-8+9-10}{12}=\dfrac{-9}{12}=\dfrac{-3}{4}\)

c: \(\left(\dfrac{3}{4}+\dfrac{-7}{2}\right)\cdot\left(\dfrac{10}{11}+\dfrac{2}{22}\right)\)

\(=\left(\dfrac{3}{4}-\dfrac{14}{4}\right)\cdot\left(\dfrac{10}{11}+\dfrac{1}{11}\right)\)

\(=-\dfrac{11}{4}\cdot1=-\dfrac{11}{4}\)

d: \(\left(\dfrac{7}{3}-\dfrac{-7}{2}\right):\left(-\dfrac{25}{6}\cdot\dfrac{1}{5}\right)\)

\(=\left(\dfrac{7}{3}+\dfrac{7}{2}\right):\dfrac{-5}{6}\)

\(=\dfrac{35}{6}\cdot\dfrac{6}{-5}=\dfrac{35}{-5}=-7\)

Answer 2

a) \(\dfrac{18}{24}+\dfrac{35}{-21}-\dfrac{1}{2}\)

\(=\dfrac{3}{4}-\dfrac{5}{3}-\dfrac{1}{2}\)

\(=\dfrac{9}{12}-\dfrac{20}{12}-\dfrac{6}{12}\)

\(=\dfrac{-17}{12}\)

b) \(\dfrac{-2}{3}-\dfrac{3}{-4}+\dfrac{5}{-6}\)

\(=\dfrac{-8}{12}+\dfrac{9}{12}-\dfrac{10}{12}\)

\(=\dfrac{-9}{12}\)

\(=\dfrac{-3}{4}\)

c) \(\left(\dfrac{3}{4}+\dfrac{-7}{2}\right).\left(\dfrac{10}{11}+\dfrac{2}{22}\right)\)

\(=\dfrac{-11}{4}.1\)

\(=\dfrac{-11}{4}\)

d) \(\left(\dfrac{7}{3}-\dfrac{-7}{2}\right):\left(-\dfrac{25}{6}.\dfrac{1}{5}\right)\)

\(=\dfrac{35}{6}:\dfrac{-5}{6}\)

\(=-7\)