a/ \(=\frac{21}{23}+\frac{125}{143}-\frac{101.21}{101.23}-\frac{1001.125}{1001.143}=0\)

b/ \(=\frac{4}{20}+\frac{8}{21}+\frac{2}{5}-\frac{3}{5}+\frac{2}{21}-\frac{10}{21}+\frac{3}{20}=\frac{7}{20}-\frac{1}{5}=\frac{4}{20}\)

c/ \(\frac{C}{2}=\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{420}=\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{20.21}\)

\(\frac{C}{2}=\frac{3-2}{2.3}+\frac{4-3}{3.4}+\frac{5-4}{4.5}+...+\frac{21-20}{20.21}=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{20}-\frac{1}{21}\)

\(\frac{C}{2}=\frac{1}{2}-\frac{1}{21}=\frac{19}{42}\Rightarrow C=\frac{19}{21}\)

a: \(C=\dfrac{-1}{2}:\dfrac{-2}{3}:\dfrac{-3}{4}\)

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

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

b: \(D=\dfrac{-6}{5}:\dfrac{-5}{4}:\dfrac{-4}{3}\)

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

\(=\dfrac{-18}{25}\)

c: \(\dfrac{4}{20}+\dfrac{16}{42}+\dfrac{6}{15}+\dfrac{-3}{5}+\dfrac{2}{21}+\dfrac{-10}{21}+\dfrac{3}{20}\)

\(=\left(\dfrac{4}{20}+\dfrac{-3}{5}+\dfrac{6}{15}\right)+\left(\dfrac{16}{42}+\dfrac{2}{21}-\dfrac{10}{21}\right)+\dfrac{3}{20}\)

\(=\left(\dfrac{1}{5}-\dfrac{3}{5}+\dfrac{2}{5}\right)+\left(\dfrac{8}{21}+\dfrac{2}{21}-\dfrac{10}{21}\right)+\dfrac{3}{20}\)

\(=\dfrac{3}{20}\)

d: \(\dfrac{42}{46}+\dfrac{250}{186}+\dfrac{-2121}{2323}+\dfrac{-125125}{143143}\)

\(=\dfrac{21}{23}+\dfrac{125}{93}+\dfrac{-21}{21}+\dfrac{-125}{143}\)

\(=\dfrac{125}{93}-\dfrac{125}{143}=\dfrac{6250}{13299}\)

\(A=-\frac{7}{21}+\left(1+\frac{1}{3}\right)\)

\(A=-\frac{1}{3}+1+\frac{1}{3}\)

\(A=\left(-\frac{1}{3}+\frac{1}{3}\right)+1=0+1=1\)

\(B=\frac{2}{15}+\left(\frac{5}{9}+\frac{-6}{9}\right)\)

\(B=\frac{2}{15}+\frac{-1}{9}=\frac{6}{45}+\frac{-5}{45}=\frac{1}{45}\)

\(C=\frac{4}{20}+\frac{16}{42}+\frac{6}{15}+\left(-\frac{3}{5}\right)+\frac{2}{21}+\left(-\frac{10}{21}\right)+\frac{3}{20}\)

\(C=\frac{1}{5}+\frac{8}{21}+\frac{2}{5}+\left(-\frac{3}{5}\right)+\frac{2}{21}+\left(-\frac{10}{21}\right)+\frac{3}{20}\)

\(C=\left(\frac{1}{5}+\frac{2}{5}+\frac{-3}{5}\right)+\left(\frac{8}{21}+\frac{2}{21}+\frac{-10}{21}\right)+\frac{3}{20}\)

\(C=0+0+\frac{3}{20}=\frac{3}{20}\)

C = \(\frac{4}{40}+\frac{16}{42}+\frac{6}{15}+\left(\frac{-3}{5}\right)+\frac{2}{21}+\left(\frac{-10}{21}\right)+\frac{3}{20}\)

C = \(\left(\frac{4}{40}+\frac{3}{20}\right)+\left(\frac{16}{42}+\frac{-10}{21}+\frac{2}{21}\right)+\left(\frac{6}{15}+\frac{-3}{5}\right)\)

C = \(\frac{1}{4}+0+\frac{-1}{5}\)

C = \(\frac{1}{20}\)

a, \(\frac{4}{20}+\frac{16}{42}+\frac{6}{15}+\frac{-3}{5}+\frac{-10}{21}+\frac{3}{20}\)

\(=\left(\frac{4}{20}+\frac{-3}{5}+\frac{6}{15}+\frac{3}{20}\right)\)\(+\left(\frac{16}{42}+\frac{2}{21}+\frac{-10}{21}\right)\)

\(=\left(\frac{4}{20}+\frac{-12}{20}+\frac{8}{20}+\frac{3}{20}\right)\)\(+\left(\frac{8}{21}+\frac{2}{21}+\frac{-10}{21}\right)\)

\(=\frac{3}{20}\)

b,\(\frac{42}{46}+\frac{250}{186}+\frac{-2121}{2323}+\frac{-125125}{143143}\)

\(=\frac{21}{23}+\frac{125}{93}+\frac{-21}{23}+\frac{-125}{143}\)

\(=\left(\frac{21}{23}+\frac{-21}{23}\right)+\left(\frac{125}{93}+\frac{-125}{143}\right)\)

\(=\frac{6250}{13299}\)

A.\(\dfrac{4}{20}\)+\(\dfrac{16}{42}\)+\(\dfrac{6}{15}\)+\(\dfrac{-3}{5}\)+\(\dfrac{2}{21}\)+\(\dfrac{-10}{21}\)+\(\dfrac{3}{20}\)

=\(\dfrac{1}{5}\)+\(\dfrac{8}{21}\)+\(\dfrac{6}{15}\)+\(\dfrac{-3}{5}\)+\(\dfrac{2}{21}\)+\(\dfrac{-10}{21}\)+\(\dfrac{3}{20}\)

=\((\dfrac{1}{5}\)+\(\dfrac{6}{15}\)+\(\dfrac{-3}{5}\)\()\)+\((\dfrac{8}{21}\)+\(\dfrac{2}{21}\)+\(\dfrac{-10}{21}\)\()\)+\(\dfrac{3}{20}\)

=\((\)\(\dfrac{1}{5}\)+\(\dfrac{2}{5}\)+\(\dfrac{-3}{5}\)\()\)+ 0 +\(\dfrac{3}{20}\)

= 0 + 0 +\(\dfrac{3}{20}\)

=\(\dfrac{3}{20}\)

B.\(\dfrac{42}{46}\)+\(\dfrac{250}{286}\)+\(\dfrac{-2121}{2323}\)+\(\dfrac{-125125}{143143}\)

=\(\dfrac{21}{23}\)+\(\dfrac{125}{143}\)+\(\dfrac{-21}{23}\)+\(\dfrac{-125}{134}\)

=\((\dfrac{21}{23}+\dfrac{-21}{23})+(\dfrac{125}{143}+\dfrac{-125}{134})\)

= 0 + 0

= 0

Chúc bạn Tran Mai học tốt nha

a)  10/17 - 5/13 -(-7)/17 - 8/13 + 11/25

=[10/17 + 7/17] - (5/13 + 3/13) + 11/25

=1-1+11/25 = 11/25

b) 4/20 + (-16)/42 - 6/15 + 3/-5 + 2/21 + 3/20 + (-10)/21

 =(4/20+3/20)  - (6/15+3/5) + (2/21+(-10)/21) + (-16)/42

=7/20  - 1 + (-8)/21 + (-16)/42

= -593/420