a)\(\dfrac{1}{2}.\dfrac{4}{3}-\dfrac{20}{3}.\dfrac{4}{5}\)

\(=\dfrac{2}{3}-\dfrac{16}{3}\)

\(=-\dfrac{14}{3}\)

b)\(\dfrac{3}{7}+\dfrac{-6}{19}+\dfrac{4}{7}+\dfrac{-13}{19}\)

\(=\left(\dfrac{3}{7}+\dfrac{4}{7}\right)+\left(\dfrac{-6}{19}+\dfrac{-13}{19}\right)\)

\(=\dfrac{7}{7}+\dfrac{-19}{19}\)

\(=1+\left(-1\right)\)

=0

b)\(\dfrac{3}{5}.\dfrac{8}{9}-\dfrac{7}{9}.\dfrac{3}{5}+\dfrac{3}{5}.\dfrac{26}{9}\)

\(=\dfrac{3}{5}.\left(\dfrac{8}{9}-\dfrac{7}{9}+\dfrac{26}{9}\right)\)

\(=\dfrac{3}{5}.\dfrac{27}{9}\)

\(=\dfrac{3}{5}.3\)

\(=\dfrac{9}{5}\)

\(\dfrac{3-1}{1.3}+\dfrac{5-3}{3.5}+\dfrac{7-5}{5.7}+...+\dfrac{101-99}{99.101}\)

\(=\dfrac{3}{1.3}-\dfrac{1}{1.3}+\dfrac{5}{3.5}-\dfrac{3}{3.5}+\dfrac{7}{5.7}-\dfrac{5}{5.7}+...+\dfrac{101}{99.101}-\dfrac{99}{99.101}\)

\(=1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{99}-\dfrac{1}{101}\)

\(=1-\dfrac{1}{101}=\dfrac{100}{101}\)

Vậy\(\dfrac{2}{1.3}+\dfrac{2}{3.5}+\dfrac{2}{5.7}+...+\dfrac{2}{99.101}=\dfrac{100}{101}\)

a) So sánh ba phân số, ta được

\(\dfrac{5}{27}< \dfrac{2}{9}< \dfrac{1}{3}\)

Vậy trong một giờ, đội thứ ba làm được ít phần công việc nhất, đội thứ hai làm được nhiều công việc nhất.

b) Nếu làm trung, cả ba đội làm được

\(\dfrac{5}{27}+\dfrac{2}{9}+\dfrac{1}{3}=\dfrac{20}{27}\)(công việc)

a)\(x-\dfrac{2}{3}=\dfrac{-5}{12}\)

\(x=\dfrac{-5}{12}+\dfrac{2}{3}\)

\(x=\dfrac{-5}{12}+\dfrac{8}{12}\)

\(x=\dfrac{\left(-5\right)+8}{12}\)

\(x=\dfrac{3}{12}\)

\(x=\dfrac{1}{4}\)

b)\(\dfrac{8}{5}:x=\dfrac{-2}{3}\)

\(x=\dfrac{8}{5}:\dfrac{-2}{3}\)

\(x=\dfrac{8}{5}.\left(\dfrac{3}{-2}\right)\)

\(x=\dfrac{-12}{5}\)

c)\(1-\dfrac{3}{7}.x=-\dfrac{2}{7}\)

\(\dfrac{3}{7}.x=1-\left(-\dfrac{2}{7}\right)\)

\(\dfrac{3}{7}.x=\dfrac{9}{7}\)

\(x=\dfrac{9}{7}:\dfrac{3}{7}\)

\(x=\dfrac{9}{7}.\dfrac{7}{3}\)

\(x=3\)

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

=\(\dfrac{-2}{7}+\dfrac{10}{35}\)

=\(\dfrac{-2}{7}=\dfrac{\left(-2\right).5}{7.5}=\dfrac{-10}{35}+\dfrac{10}{35}\)

=0

b)\(\dfrac{-8}{19}+\dfrac{-4}{21}-\dfrac{17}{21}+\dfrac{27}{19}\)=\(\dfrac{-8}{19}+\dfrac{-4}{21}+\dfrac{-17}{21}+\dfrac{27}{19}\)

=\(\left(\dfrac{-8}{19}+\dfrac{27}{19}\right)+\left(\dfrac{-4}{21}+\dfrac{-17}{21}\right)\)

=\(\dfrac{\left(-8\right)+27}{19}+\dfrac{\left(-4\right)+\left(-17\right)}{21}\)

=\(\dfrac{19}{19}+\dfrac{-21}{21}\)

=1+(-1)

=1-1

=0

b)\(\dfrac{6}{5}.\dfrac{3}{13}-\dfrac{6}{5}.\dfrac{16}{13}=\dfrac{6}{5}.\left(\dfrac{3}{13}-\dfrac{16}{13}\right)\)

\(=\dfrac{6}{5}.\left(\dfrac{3-6}{13}\right)\)

\(=\dfrac{6}{5}.\left(\dfrac{-13}{13}\right)\)

\(=\dfrac{6}{5}.\left(-1\right)\)

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