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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

`Answer:`

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

\(=\left(\frac{4}{20}+\frac{3}{20}+\frac{6}{15}\right)+\left(\frac{8}{21}+\frac{3}{21}-\frac{10}{21}\right)\)

\(=\frac{3}{4}+\frac{1}{21}\)

\(=\frac{67}{84}\)

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

\(=\frac{21}{23}+\frac{125}{93}+\left(-\frac{21}{23}\right)+\left(-\frac{125}{43}\right)\)

\(=\left(\frac{21}{23}+-\frac{21}{23}\right)+\left(\frac{125}{93}+-\frac{125}{43}\right)\)

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

a, 5/-14. 7/-19=8/38

b, -15/4 .( 16/-25 )=12/5

c, 3/-10 .( -15/-2 )=

d, -5/7 . ( 21/-10 )=-9/4

e, 10/-3. (6/-5)==4

f, 21/-9 . ( -6/14 )=1

g, -10/9 . ( 36/20 )=-2

a, 4/20+16/42+6/15+-3/5+2/2+-10/21=1/5+8/21+2/5+-3/5+2/2+-16/21=(1/5+2/5+-3/5)+(8/21=-16/21)+1=-2/21+1=-19/21                       b,42/46+250/186+-2121/2323+-125125/143143                                                                                                                                =21/23+125/93+-21/23+-125/143                                                                                                                                                   =(21/23+-21/23)+(-125/143+125/93)                                                                                                                                              =6250/13299