Các cặp phân số đối nhau là:

\(\frac{{ - 5}}{6}\) và \(\frac{5}{6}\) (vì \(\frac{{ - 5}}{6}+\frac{5}{6}=0\))

\(\frac{{ - 40}}{{ - 10}}\) và \(\frac{{40}}{{ - 10}}\) (vì \(\frac{{ - 40}}{{ - 10}}+\frac{{40}}{{ - 10}}=4+(-4)=0\))

\(\frac{5}{6}\) và \(\frac{{10}}{{ - 12}}\) (vì \(\frac{5}{6} +\frac{{10}}{{ - 12}}=0\))

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

\(\dfrac{-40}{-10};\dfrac{40}{-10}\)

\(\dfrac{10}{-12};\dfrac{5}{6}\)

\(\frac{\frac{3}{8}-\frac{3}{10}+\frac{3}{11}+\frac{3}{12}}{\frac{5}{8}-\frac{5}{10}+\frac{5}{11}+\frac{5}{12}}+\frac{\frac{3}{2}+1+\frac{3}{4}}{\frac{5}{2}+\frac{5}{3}+\frac{5}{4}}\)

\(=\frac{3.\left(\frac{1}{8}-\frac{1}{10}+\frac{1}{11}+\frac{1}{12}\right)}{5.\left(\frac{1}{8}-\frac{1}{10}+\frac{1}{11}+\frac{1}{12}\right)}+\frac{3.\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}\right)}{5.\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}\right)}\)

\(=\frac{3}{5}+\frac{3}{5}\)

\(=\frac{6}{5}\)

\(\frac{6:\frac{3}{5}-1\frac{1}{6}.\frac{6}{7}}{\frac{4}{5}.\frac{10}{11}+5\frac{2}{12}}\)

\(=\frac{10-\frac{7}{6}.\frac{6}{7}}{\frac{8}{11}+\frac{31}{6}}\)

\(=\frac{10-1}{\frac{389}{66}}\)

\(=\frac{9}{\frac{389}{66}}\)

\(=\frac{594}{389}\)

1/2926

Ta có : 

\(\frac{6:\frac{3}{5}-1\frac{1}{6}.\frac{6}{7}}{\frac{4}{5}.\frac{10}{11}+5\frac{2}{12}}\)

\(=\frac{6.\frac{5}{3}-\frac{7}{6}.\frac{6}{7}}{\frac{8}{11}+5\frac{1}{6}}\)

\(=\frac{10-1}{\frac{8}{11}+\frac{31}{6}}\)

\(=\frac{9}{\frac{48}{66}+\frac{341}{66}}\)

\(=\frac{9}{\frac{389}{66}}\)

\(=9.\frac{66}{389}\)

\(=\frac{594}{389}\)

P/s : Số hơi to

~ Ủng hộ nhé 

S = 1/5 = 2/10

Vì 2/10 < 3/10 => S < 3/10 (đpcm)

Ai k mk mk k lại cho !!

\(S=\frac{\frac{1}{4}+\frac{1}{6}+\frac{1}{10}}{5\cdot\left(\frac{1}{4}+\frac{1}{6}+\frac{1}{10}\right)}\)

\(S=\frac{1}{5}\)

\(\frac{1}{5}<\frac{3}{10}\)

\(S<\frac{3}{10}\)

S=\(\frac{\frac{1}{4}+\frac{1}{6}+\frac{1}{10}}{\frac{5}{4}+\frac{5}{6}+\frac{5}{10}}\)

=\(\frac{\frac{1}{4}+\frac{1}{6}+\frac{1}{10}}{5.\left(\frac{1}{4}+\frac{1}{6}+\frac{1}{10}\right)}\)

=\(\frac{1}{5}=\frac{2}{10}<\frac{3}{10}\)

Ta có : 

\(S=\frac{3}{2}+\frac{4}{3}+\frac{5}{4}+\frac{6}{5}+\frac{7}{6}+\frac{8}{7}+\frac{9}{8}+\frac{10}{9}+\frac{11}{10}+\frac{12}{11}\)

\(S=\frac{2+1}{2}+\frac{3+1}{3}+\frac{4+1}{4}+...+\frac{11+1}{11}\)

\(S=\left(1+\frac{1}{2}\right)+\left(1+\frac{1}{3}\right)+\left(1+\frac{1}{4}\right)+...+\left(1+\frac{1}{11}\right)\)

\(S=\left(1+1+1+...+1\right)+\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{11}\right)\)

\(S=10+\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{11}\right)>10\) 

\(\Rightarrow\)\(S>10\) 

Vậy \(S>10\)

Chúc bạn học tốt ~ 

\(\frac{6\div\frac{3}{5}-1\frac{1}{6}\times\frac{6}{7}}{4\frac{1}{5}\times\frac{10}{11}+5\frac{2}{11}}=\frac{6\div\frac{3}{5}-\frac{1\times6+1}{6}\times\frac{6}{7}}{\frac{4\times5+1}{5}\times\frac{10}{11}+\frac{5\times11+2}{11}}\)

\(=\frac{6\div\frac{3}{5}-\frac{7}{6}\times\frac{6}{7}}{\frac{21}{5}\times\frac{10}{11}+\frac{57}{11}}=\frac{\left(6\div\frac{3}{5}\right)-\left(\frac{7}{6}\times\frac{6}{7}\right)}{\left(\frac{21}{5}\times\frac{10}{11}\right)+\frac{57}{11}}\)

\(=\frac{10-1}{\frac{42}{11}+\frac{57}{11}}=\frac{9}{\frac{99}{11}}=\frac{9}{9}=1\)

\(\frac{5}{6}\)+ \(\frac{7}{8}\)= \(\frac{20}{24}\)+\(\frac{21}{24}\)=\(\frac{41}{24}\)

\(\frac{9}{10}\)x\(\frac{5}{6}\)=\(\frac{3x3}{2x5}\)x\(\frac{5}{3x2}\)=\(\frac{3}{4}\)

\(\frac{5}{8}\)-\(\frac{2}{5}\)=\(\frac{25}{40}\)-\(\frac{16}{40}\)=\(\frac{9}{40}\)

\(\frac{6}{5}\)/\(\frac{3}{7}\)=\(\frac{6}{5}\)x\(\frac{7}{3}\)=\(\frac{42}{15}\)