a, \(=\dfrac{2}{9}-\dfrac{10}{10}=\dfrac{2}{9}-1=-\dfrac{7}{9}\)

b, \(=-\dfrac{12}{6}+\dfrac{2}{5}=-2+\dfrac{2}{5}=-\dfrac{8}{5}\)

c, \(=\dfrac{27}{13}-1=\dfrac{14}{13}\)

d, \(=\dfrac{12}{11}+\dfrac{7}{19}+\dfrac{12}{19}=\dfrac{12}{11}+1=\dfrac{23}{11}\)

a) \(\dfrac{2}{9}+\dfrac{-3}{10}+\dfrac{-7}{10}\)

\(=\dfrac{2}{9}+\dfrac{-10}{10}=\dfrac{2}{9}-1=-\dfrac{7}{9}\)

b) \(\dfrac{-11}{6}+\dfrac{2}{5}+\dfrac{-1}{6}\)

\(=-2+\dfrac{2}{5}=-\dfrac{8}{5}\)

f: \(=\dfrac{7}{19}\left(\dfrac{8}{11}+\dfrac{3}{11}\right)-\dfrac{12}{19}=\dfrac{7}{19}-\dfrac{12}{19}=\dfrac{-5}{19}\)

i: \(=\left(\dfrac{9}{24}-\dfrac{18}{24}+\dfrac{14}{24}\right)\cdot\dfrac{6}{5}+\dfrac{1}{2}=\dfrac{5}{24}\cdot\dfrac{6}{5}+\dfrac{1}{2}\)

=1/4+1/2=3/4

` 7/19 . 8/11 + 3/11 . 7/19 + (-12)/19 `

`= 7/19 . ( 8/11 + 3/11 ) + (-12)/19 `

`= 7/19 . 11/11 + (-12)/19`

`= 7/19 . 1 + (-12)/19 `

`= 7/19 + (-12)/19 `

`= -5/19 `

`( 3/8 + (-3)/4 + 7/12 ) : 5/6 + 1/2`

`= 3/8 + (-3)4 + 7/12 . 6/5 + 1/2`

`= ( 9+(-18) + 14)/24 . 6/5 + 1/2`

`= 5/24 . 6/5 + 1/2`

`= 1/4 + 1/2 `

`= 3/4`

g: \(=\dfrac{-3}{4}-\dfrac{1}{4}+\dfrac{5}{7}+\dfrac{2}{7}+\dfrac{3}{5}=\dfrac{3}{5}\)

h: \(=\dfrac{7}{19}\left(\dfrac{8}{11}+\dfrac{3}{11}\right)-\dfrac{12}{19}=\dfrac{7}{19}-\dfrac{12}{19}=-\dfrac{5}{19}\)

i: \(=\dfrac{2013}{7}\left(19+\dfrac{5}{8}-26-\dfrac{5}{8}\right)=\dfrac{2013}{7}\cdot\left(-7\right)=-2013\)

Gợi ý: Sử dụng tính chất phân phối của phép nhân đối với phép cộng để nhóm thừa số chung ra ngoài.

\(=\dfrac{4}{19}\left(\dfrac{-5}{6}-\dfrac{7}{12}-\dfrac{10}{3}\right)\)

\(=\dfrac{4}{19}\cdot\left(\dfrac{-10-7-40}{12}\right)=\dfrac{4}{19}\cdot\dfrac{-57}{12}=-\dfrac{3}{3}=-1\)

=\(\dfrac{4}{19}.\left(-\dfrac{5}{6}+-\dfrac{7}{12}\right)-\dfrac{40}{57}\)

=\(-\dfrac{4}{19}-\dfrac{40}{57}\)

=\(-\dfrac{52}{57}\)

\(a.\)

\(\dfrac{27}{13}-\dfrac{106}{111}+-\dfrac{5}{111}=\dfrac{27}{13}-\dfrac{106}{111}-\dfrac{5}{111}=\dfrac{27}{13}-\left(\dfrac{106+6}{111}\right)=\dfrac{27}{13}-1=\dfrac{14}{13}\)

\(b.\)

\(\dfrac{12}{11}-\dfrac{-7}{19}+\dfrac{12}{19}=\dfrac{12}{11}+\dfrac{7}{19}+\dfrac{12}{19}=\dfrac{12}{11}+1=\dfrac{23}{11}\)

\(c.\)

\(\dfrac{5}{17}-\dfrac{25}{31}+\dfrac{12}{17}+-\dfrac{6}{31}=\left(\dfrac{5}{17}+\dfrac{12}{17}\right)-\left(\dfrac{25}{31}+\dfrac{6}{31}\right)=1-1=0\)

a) \(\dfrac{27}{13}-\dfrac{106}{111}+\dfrac{-5}{111}=\dfrac{27}{13}+\left(\dfrac{-106}{111}+\dfrac{-5}{111}\right)=\dfrac{27}{13}+-1=\dfrac{14}{13}\) 

b) \(\dfrac{12}{11}-\dfrac{-7}{19}+\dfrac{12}{19}=\dfrac{12}{11}+\left(\dfrac{7}{19}+\dfrac{12}{19}\right)=\dfrac{12}{11}+1=\dfrac{23}{11}\) 

c)\(\dfrac{5}{17}-\dfrac{25}{31}+\dfrac{12}{17}+\dfrac{-6}{31}=\left(\dfrac{5}{17}+\dfrac{12}{17}\right)+\left(\dfrac{-25}{31}+\dfrac{-6}{31}\right)=1+-1=0\)

a: \(\frac23+\left(\frac57+\frac{-2}{3}\right)\)

\(=\frac23+\frac57-\frac23\)

\(=\frac57\)

b: \(\left(-\frac14+\frac58\right)+\frac{-3}{8}\)

\(=\frac{-2}{8}+\frac58+\frac{-3}{8}\)

=0

c: \(\frac75\cdot\frac{8}{19}+\frac75\cdot\frac{12}{19}-\frac75\cdot\frac{1}{19}\)

\(=\frac75\left(\frac{8}{19}+\frac{12}{19}-\frac{1}{19}\right)\)

\(=\frac75\cdot\frac{19}{19}=\frac75\)

d: \(6\frac{3}{10}-\left(3\frac47+2\frac{3}{10}\right)\)

\(=6+\frac{3}{10}-3-\frac47-2-\frac{3}{10}\)

\(=1-\frac47=\frac77-\frac47=\frac37\)

e: \(\left(31,12-5,97\right)-\left(-68,88+4,03\right)\)

=31,12-5,97+68,88-4,03

=100-10

=90

f: \(3,7\cdot\left(-10,56\right)+3,7\cdot110,56\)

\(=3,7\cdot\left(-10,56+110,56\right)\)

\(=3,7\cdot100=370\)

\(\dfrac{{ - 7}}{{12}} + \dfrac{5}{{12}} = \dfrac{{ - 7 + 5}}{{12}} = \dfrac{{ - 2}}{{12}} =  \dfrac{{ - 1}}{{6}}\) ;   

\(\dfrac{{ - 8}}{{11}} + \dfrac{{ - 19}}{{11}} = \dfrac{{ - 8 + \left( { - 19} \right)}}{{11}} = \dfrac{{ - 27}}{{11}}\)

\(A=\dfrac{636363\cdot37-373737\cdot63}{1+2+3+...+2006}\)

\(=\dfrac{37^2\cdot3^3\cdot7^2\cdot13-37^2\cdot3^3\cdot7^2\cdot13}{\left(2006+1\right)\cdot1003}\)

=0