a.$17\cdot (29-(-111\left)\right]+29\cdot (-17)$ 

$=17\cdot (29+111)-29\cdot 17$

$=17\cdot (29+111-29)$

$=17\cdot (29-29+111)$

$=17\cdot 111$

$=2997$

b.$19\cdot 43+(-20)\cdot 43-(-40)$

$=19\cdot 43-20\cdot 43+40$

$=43(19-20)+40$

$=43\cdot (-1)+40$

$=-43+40$

$=-3$

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\(a.\)

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

\(b.\)

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

\(c.\)

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

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) 4.(1 930 + 2 019) + 4.(-2 019)

= 4.(1 930 + 2 019 - 2 019)

= 4.1 930

= 7 720

b) (-3).(-17) + 3.(120 - 17)

= 3.17 + 3.(120 - 17)

= 3.(17 + 120 - 17)

= 3.120

= 360

a) 12 + 13 + 14 - 15 - 16 - 17

= (12 - 15) + (13 - 16) + (14 - 17)

= (-3) + (-3) + (-3) = -9

b) (35 - 17) - (25 - 7 + 22)

= 35 - 17 - 25 + 7 - 22

= (35 - 25) - (17 - 7) - 22

= 10 - 10 - 22 = -22

\(a)\left(-17\right)+\left(-23\right)+44=-40+44=4\)

\(b)\left(-39\right)+\left(-16\right)+39=\left[\left(-39\right)+39\right]+\left(-16\right)=0+\left(-16\right)=-16\)

a) (- 17) + (- 23) + 44;

= (- 40) + 44

= 4

b) (- 39) + (- 16) + 39.

= (- 39) + 39 + (- 16)

= 0 + (- 16)

= - 16

a) (- 17) + (- 23) + 44

=  [ (- 17) + (- 23) ] + 44 

=  (- 40) + 44

= 4

b) (- 39) + (- 16) + 39

= [ (- 39) + 39 ] + (- 16)

= 0 + (- 16)

= -16

17.[29 - (-111) + 29.(-17)]

= 17.[29 + 111 + 29.(-17)]

= 17.[29 + 111 + (-493)

= 17.[140 + (-493)]

= 17.(-353)

= -6001.

39(29 - 17) - 29(39 - 17)

= 39.29 - 39.17 - 29.39 + 29.17

= -39.17 + 29.17

= 17(-39 + 29)

= 17.(-10)

= -170

\(a,\left(4+32+6\right)+\left(10-32-2\right)\\ =\left(10+32\right)+\left(10-32-2\right)\\ =10+32+10-32-2\\ =20-2\\ =18\\ b,300:4+300:6-25\\ =300:\left(4+6\right)-25\\ =300:10-25\\ =30-25\\ =5\\ c,17.\left[29-\left(-111\right)\right]+29.\left(-17\right)\\ =17.\left(29+111\right)+29.\left(-1\right).17\\ =17.\left(29+111-29\right)\\ =17.111=1887\\ d,19.43+\left(-20\right).43-\left(-40\right)\\ =19.43+\left(-20\right).43+40\\ =43.\left(19-20\right)+40\\ =-43+40\\ =-3\)

17[21-(-111)]+17[29-121]=17.132+17.(-92)=17.[132+(-92)]=17.40=680