a) \(A=\dfrac{3}{5}.\dfrac{6}{7}+\dfrac{3}{7}.\dfrac{3}{5}-\dfrac{2}{7}.\dfrac{3}{5}\)

    \(A=\dfrac{3}{5}.\dfrac{6}{7}+\dfrac{3}{5}.\dfrac{3}{7}-\dfrac{2}{7}.\dfrac{3}{5}\)

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

    \(A=\dfrac{3}{5}.1\)

    \(A=\dfrac{3}{5}\)

b) \(B=\left(-13.\dfrac{2}{5}+\dfrac{-2}{9}:2\dfrac{1}{2}+\dfrac{2}{5}.\dfrac{11}{9}\right).2\dfrac{1}{2}\)

    \(B=\left(-13.\dfrac{2}{5}+\dfrac{-2}{9}:\dfrac{5}{2}+\dfrac{2}{5}.\dfrac{11}{9}\right).\dfrac{5}{2}\)

    \(B=\left(-13.\dfrac{2}{5}+\dfrac{-2}{9}.\dfrac{5}{2}+\dfrac{2}{5}.\dfrac{11}{9}\right).\dfrac{5}{2}\)

    \(B=\left(-13+\dfrac{-2}{9}+\dfrac{11}{9}\right).\dfrac{2}{5}.\dfrac{5}{2}\)

    \(B=-13+\left(\dfrac{-2}{9}+\dfrac{11}{9}\right)\)

    \(B=-13+1\)

    \(B=-12\)

c) \(C=\left(\dfrac{-4}{5}+\dfrac{5}{7}\right):\dfrac{2}{3}+\left(\dfrac{-1}{5}-\dfrac{2}{7}\right):\dfrac{2}{3}\)

    \(C=\left(\dfrac{-4}{5}+\dfrac{5}{7}\right).\dfrac{3}{2}+\left(\dfrac{-1}{5}-\dfrac{2}{7}\right).\dfrac{3}{2}\)

    \(C=\left(\dfrac{-4}{5}+\dfrac{5}{7}+\dfrac{-1}{5}-\dfrac{2}{7}\right).\dfrac{3}{2}\)

    \(C=\left(\dfrac{-4}{5}+\dfrac{-1}{5}+\dfrac{5}{7}+\dfrac{2}{7}\right).\dfrac{3}{2}\)

    \(C=\left(-1+1\right).\dfrac{3}{2}\)

    \(C=0.\dfrac{3}{2}\)

    \(C=0\)

d) \(D=\dfrac{4}{9}:\left(\dfrac{1}{15}-\dfrac{2}{3}\right)+\dfrac{4}{9}:\left(\dfrac{1}{11}-\dfrac{5}{22}\right)\)

     \(D=\dfrac{4}{9}:\left(\dfrac{1}{15}-\dfrac{10}{15}\right)+\dfrac{4}{9}:\left(\dfrac{2}{22}-\dfrac{5}{22}\right)\)

     \(D=\dfrac{4}{9}:\dfrac{-3}{5}+\dfrac{4}{9}:\dfrac{-3}{22}\)

     \(D=\dfrac{4}{9}.\dfrac{-5}{3}+\dfrac{4}{9}.\dfrac{-22}{3}\)

     \(D=\dfrac{4}{9}.\left(\dfrac{-5}{3}+\dfrac{-22}{3}\right)\)

     \(D=\dfrac{4}{9}.\left(-9\right)\)

     \(D=-4\)

a) \(P=\dfrac{2}{3}-\left(-\dfrac{1}{4}\right)+\dfrac{3}{5}-\dfrac{7}{45}-\left(-\dfrac{5}{9}\right)+\dfrac{1}{12}+\dfrac{1}{35}\)

    \(P=\dfrac{2}{3}+\dfrac{1}{4}+\dfrac{3}{5}-\dfrac{7}{45}+\dfrac{5}{9}+\dfrac{1}{12}+\dfrac{1}{35}\)

    \(P=\left(\dfrac{2}{3}+\dfrac{1}{4}+\dfrac{1}{12}\right)+\left(\dfrac{3}{5}-\dfrac{7}{45}+\dfrac{5}{9}\right)+\dfrac{1}{35}\)

    \(P=1+1+\dfrac{1}{35}\)

    \(P=2+\dfrac{1}{35}\)

    \(P=\dfrac{70+1}{35}\)

    \(P=\dfrac{71}{35}\)

b) \(Q=\left(5-\dfrac{3}{4}+\dfrac{1}{5}\right)-\left(6+\dfrac{7}{4}-\dfrac{8}{5}\right)-\left(2-\dfrac{5}{4}+\dfrac{16}{5}\right)\)

    \(Q=5-0,75+0,2-6-1,75+1,6-2+1,25-3,2\)

    \(Q=\left(5-6-2\right)-\left(0,75+1,75-1,25\right)+\left(0,2+1,6-3,2\right)\)

    \(Q=-3-1,25+\left(-1,4\right)\)

    \(Q=-4,25+\left(-1,4\right)\)

    \(Q=-5,65\)

a) \(A=\left(\dfrac{1}{3}-\dfrac{8}{15}-\dfrac{1}{7}\right)+\left(\dfrac{2}{3}+\dfrac{-7}{15}+1\dfrac{1}{7}\right)\)

    \(A=\dfrac{1}{3}-\dfrac{8}{15}-\dfrac{1}{7}+\dfrac{2}{3}+\dfrac{-7}{15}+\dfrac{8}{7}\)

    \(A=\left(\dfrac{1}{3}+\dfrac{2}{3}\right)-\left(\dfrac{8}{15}-\dfrac{-7}{15}\right)+\left(\dfrac{8}{7}-\dfrac{1}{7}\right)\)

    \(A=1-1+1\)

    \(A=1\)

b) \(B=0,25+\dfrac{3}{5}-\left(\dfrac{1}{8}-\dfrac{2}{5}+1\dfrac{1}{4}\right)\)

    \(B=0,25+0,6-\left(0,125-0,4+\dfrac{5}{4}\right)\)

    \(B=0,25+0,6-\left(0,125-0,4+1,25\right)\)

    \(B=0,25+0,6-0,125+0,4-1,25\)

    \(B=\left(0,25-1,25\right)+\left(0,6+0,4\right)-0,125\)

    \(B=-1+1-0,125\)

    \(B=-0,125\)