\(\begin{array}{l}B = \dfrac{{ - 1}}{9} + \dfrac{8}{7} + \dfrac{{10}}{9} + \dfrac{{ - 29}}{7}\\ = \left( {\dfrac{{ - 1}}{9} + \dfrac{{10}}{9}} \right) + \left( {\dfrac{8}{7} + \dfrac{{ - 29}}{7}} \right)\\ = \dfrac{9}{9} + \dfrac{{ - 21}}{7} = 1 - 3 =  - 2\end{array}\)

^{1/2 + 2/3 - 3/4 * 4/5 * 5/6 * 6/7 * 7/8 * 8/9 *...* 29/30 : 6/10}

^{= 1/2 + 2/3 - 1/10 : 6/10}

^{= 1/2 + 2/3 - 1/6}

^{= 1}

\(a.\dfrac{-3}{8}-\dfrac{13}{65}+\dfrac{3}{8}=\left(\dfrac{3}{8}-\dfrac{3}{8}\right)-\dfrac{13}{65}=-\dfrac{13}{65}\)

\(b.\left(\dfrac{-13}{7}-\dfrac{4}{9}\right)-\left(-\dfrac{10}{7}-\dfrac{4}{9}\right)=\dfrac{-13}{7}-\dfrac{4}{9}+\dfrac{10}{7}+\dfrac{4}{9}\\ =\left(\dfrac{-13}{7}+\dfrac{10}{7}\right)+\left(\dfrac{4}{9}-\dfrac{4}{9}\right)=-\dfrac{3}{7}\)

\(c.17\dfrac{1}{3}\cdot\left(\dfrac{-3}{7}\right)+3\dfrac{2}{3}\cdot\left(\dfrac{-3}{7}\right)=\dfrac{-3}{7}\cdot\left(17\dfrac{1}{3}+3\dfrac{2}{3}\right)\\ =\dfrac{-3}{7}\cdot\left(\dfrac{52}{3}+\dfrac{11}{3}\right)=\dfrac{-3}{7}\cdot21=-9\)

\(=20.\left(-9\right)+\left(-20\right).21\)

\(=-180+\left(-420\right)\)

\(=-600\)

a) =20.(-9)+(-20).21

=20.(-9)+20.(-21)

=20[(-9)+(-21)]

=20.(-30)

=-600

Cách 1: Theo kiểu dài                       |           Cách 2:Ngắn gọn
a) (29 – 9). (-9) + (-13 – 7). 21          |       a) (29-9) . (-9) + (-13-7) . 21
= 20. (-9) + [- (13 + 7). 21]                 |       =20.(-9)+(-20).21
= 20. (-9) + (-20). 21                          |       =180+(-420)
= (-20). 9 + (-20). 21                          |       =600
= (-20). (9 + 21)                                 |
= (-20). 30                                          |
= - (20. 30)                                         |
= - 600.                                              |

(Chúc bạn học tốt nha~!)

\(B=-\left(1+4+7+...+100\right)\\ B=-\dfrac{\left(100+1\right)\left[\left(100-1\right):3+1\right]}{2}=-\dfrac{101\cdot34}{2}=-1717\\ C=10+10+10+10-103=50-103=-53\)

\(a.\)

\(\dfrac{2}{9}+\dfrac{-3}{10}+-\dfrac{7}{10}=\dfrac{2}{9}-1=\dfrac{2}{9}-\dfrac{9}{9}=-\dfrac{7}{9}\)

\(b.\)

\(\dfrac{-11}{6}+\dfrac{2}{5}+\dfrac{-1}{6}=\left(-\dfrac{11}{6}+-\dfrac{1}{6}\right)+\dfrac{2}{5}=-2+\dfrac{2}{5}=\dfrac{-10}{5}+\dfrac{2}{5}=\dfrac{-8}{5}\)

\(c.\)

\(-\dfrac{5}{8}+\dfrac{12}{7}+\dfrac{13}{8}+\dfrac{2}{7}=\left(-\dfrac{5}{8}+\dfrac{13}{8}\right)+\left(\dfrac{12}{7}+\dfrac{2}{7}\right)=1+2=3\)

a: =382-282+531-331

=100+200=300

b: =(7-8)+(9-10)+...+(2009-2010)

=(-1)+(-1)+....+(-1)

=-1002

c: =-(1+2+3+...+2009+2010)

=-2010*2011/2=-2021055

a) 152 + (-73) - (-18) - 127 = 152 – 73 +18 -127

= (152 + 18) – (127 + 73) = 170 - 200 = -(200 - 170) = -30

b) 7 + 8 + (-9)  + (-10) = (7 + 8) + [(-9)  + (-10)]

= 15 + (-19) = -(19 - 15) = -4.