\(\text{(−1)+(−3)+...+(−199)+(−201)(−1)+(−3)+...+(−199)+(−201)}\)

=\(\text{−(1+3+...+199+201)=−(1+3+...+199+201)}\)

=\(\dfrac{\left(201+1\right).\left[\left(201-1\right)\right]:2+1}{2}\)

= \(\dfrac{-200.102}{2}=\dfrac{-20400}{2}=-10200\)

\(\text{17 + ( − 20 ) + 23 + ( − 26 ) + . . . + 53 + ( − 56 ) = [ 17 + ( − 20 ) ] + [ 23 + ( − 26 ) ] + . . . + [ 53 + ( − 56 ) ] = ( − 3 ) + ( − 3 ) + . . . + ( − 3 ) = ( − 3 ) . ( 7 ) = − 21}\)

\(\text{=17 + ( − 20 ) + 23 + ( − 26 ) + . . . + 53 + ( − 56 ) = [ 17 + ( − 20 ) ] + [ 23 + ( − 26 ) ] + . . . + [ 53 + ( − 56 ) ] = ( − 3 ) + ( − 3 ) + . . . + ( − 3 ) = ( − 3 ) . ( 7 ) = − 21}\)

 \(\text{ = ( − 3 ) + ( − 3 ) + . . . + ( − 3 )}\)

\(\text{= ( − 3 ) . ( 7 ) = − 21}\)

a)  5/17 * 8/-7+8/17*-7/3+-7/3*4/17

-40/119 + 12/17 × -7/3

-40/119 + -28/17 =-236/119

b) -10/13 + 5/17 - 3/13 + 12/17 - 11/20

(5/17+12/17)-(10/13+3/13)-11/20

-11/20

a)  5/17 * 8/-7+8/17*-7/3+-7/3*4/17

-40/119 + 12/17 × -7/3

-40/119 + -28/17 =-236/119

b) -10/13 + 5/17 - 3/13 + 12/17 - 11/20

(5/17+12/17)-(10/13+3/13)-11/20

-11/20

\(1)\)\(-\dfrac{10}{11}.\dfrac{8}{9}+\dfrac{7}{18}.\dfrac{10}{11}\)

\(=\dfrac{10}{11}\left(-\dfrac{8}{9}+\dfrac{7}{18}\right)\)

\(=\dfrac{10}{11}\left(\dfrac{-16}{18}+\dfrac{7}{18}\right)\)

\(=\dfrac{10}{11}.\left(-\dfrac{1}{2}\right)=-\dfrac{5}{11}\)

\(2)\)\(\dfrac{12}{25}.\dfrac{23}{7}-\dfrac{12}{7}.\dfrac{13}{25}\)

\(=\dfrac{12}{7}.\dfrac{23}{25}-\dfrac{12}{7}.\dfrac{13}{25}\)

\(=\dfrac{12}{7}.\left(\dfrac{23}{25}-\dfrac{13}{25}\right)\)

\(=\dfrac{12}{7}.\dfrac{2}{5}=\dfrac{24}{35}\)

\(3)\)\(\dfrac{3}{7}.\dfrac{16}{15}-\dfrac{2}{15}.\dfrac{-3}{7}\)

\(=\dfrac{3}{7}.\dfrac{16}{15}-\dfrac{3}{7}.\dfrac{-2}{15}\)

\(=\dfrac{3}{7}.\left(\dfrac{16}{15}+\dfrac{2}{15}\right)\)

\(=\dfrac{3}{7}.\dfrac{18}{15}=\dfrac{18}{35}\)

\(4)\)\(-\dfrac{4}{13}.\dfrac{5}{17}+\dfrac{-12}{13}.\dfrac{4}{17}\)

\(=-\dfrac{4}{13}.\dfrac{5}{17}+\dfrac{-4}{13}.\dfrac{12}{17}\)

\(=-\dfrac{4}{13}.\left(\dfrac{5}{17}+\dfrac{12}{17}\right)\)

\(=-\dfrac{4}{13}.\dfrac{17}{17}=-\dfrac{4}{13}\)

`#040911`

`1)`

`-10/11 * 8/9 + 7/18 . 10/11`

`= 10/11 * (-8/9 + 7/18)`

`= 10/11 * (-1/2)`

`= -5/11`

`2)`

`12/25 * 23/7 - 12/7 *13/25`

`= 12/7 * 23/25 - 12/7 * 13/25`

`= 12/7 * (23/25 - 13/25)`

`= 12/7 * 2/5`

`= 24/35`

`3)`

`3/7 * 16/15 - 2/15 * (-3)/7`

`= 3/7 * (16/15 + 2/15)`

`= 3/7 * 6/5`

`= 18/35`

`4)`

`-4/13 * 5/17 + (-12)/13 * 4/17`

`= -4/17 * 5/13 + (-12)/13 * 4/17`

`= 4/17 * (-5/13 - 12/13)`

`= 4/17 * (-17)/13`

`= -4/13`

\(a)\)Ta tách thành 2 vế của phép tính ra thành:

\(\left(5+7+9+11+13+15+17\right)+\left(3+8+13+18+23+28\right)\)

Ta gọi dãy \(\left(5+7+9+11+13+15+17\right)\)là \(S_1\)

\(\left(3+8+13+18+23+28\right)\) là dãy \(S_2\)

- Số số hạng của dãy \(S_1\)là:

\(\left(17-5\right)\div2+1=7\)( số hạng )

Tổng của dãy \(S_1\)là:

\(\left(17+5\right)\times7\div2=77\)

- Số số hạng của dãy \(S_2\)là:\(\left(3+8+13+18+23+28\right)\)

\(\left(28-3\right)\div5+1=6\)( số hạng )

Tổng của dãy \(S_2\)là:

\(\left(28+3\right)\times6\div2=93\)

Tổng của dãy \(S_1\)và \(S_2\)là:

\(77+93=170\)

Đáp số: \(170\)

\(b)\)Ta ghép thành 2 vế của phép tính ra thành:

\(\left(4+7+10+13+16+19\right)+\left(5+9+13+17+21+25\right)\)

Ta gọi dãy \(\left(4+7+10+13+16+19\right)\)là \(S_1\)

\(\left(5+9+13+17+21+25\right)\)là \(S_2\)

- Số số hạng của dãy số \(S_1\)là

\(\left(19-4\right)\div3+1=6\)( số hạng )

Tổng của dãy số \(S_1\)là:

\(\left(19+4\right)\times6\div2=69\)

- Số số hạng của dãy \(S_2\)là:\(\left(5+9+13+17+21+25\right)\)

\(\left(25-5\right)\div4+1=6\)( số hạng )

Tổng của dãy số \(S_2\)là:

\(\left(25+5\right)\times6\div2=90\)

Tổng của dãy \(S_1\)  và \(S_2\)là:

\(69+90=159\)

Đáp số: \(159\)

\(\dfrac{17}{6}-\dfrac{8}{5}+\dfrac{2}{10}=\dfrac{85}{30}-\dfrac{48}{30}+\dfrac{6}{30}=\dfrac{31}{30}\)

3--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

=1+(2-3-4+5)+(6-7-8+9)+...+(2010-2011-2012+2013)+(2014-2015-2016)

=1+0+0+...+0+(-2017)

=1+(-2017)

=-2016

Thank You Very Much!!!

Giải:

a) \(2\dfrac{17}{20}-1\dfrac{15}{11}+6\dfrac{9}{20}:3\)

\(=\dfrac{57}{20}-\dfrac{26}{11}+\dfrac{129}{20}:3\) 

\(=\dfrac{107}{220}+\dfrac{43}{20}\)

\(=\dfrac{29}{11}\)

b) \(4\dfrac{3}{7}:\left(\dfrac{7}{5}.4\dfrac{3}{7}\right)\) 

\(=\dfrac{31}{7}:\left(\dfrac{7}{5}.\dfrac{31}{7}\right)\) 

\(=\dfrac{31}{7}:\dfrac{31}{5}\) 

\(=\dfrac{5}{7}\) 

c) \(\left(3\dfrac{2}{9}.\dfrac{15}{23}.1\dfrac{7}{29}\right):\dfrac{5}{23}\) 

\(=\left(\dfrac{29}{9}.\dfrac{15}{23}.\dfrac{36}{29}\right):\dfrac{5}{23}\) 

\(=\dfrac{60}{23}:\dfrac{5}{23}\) 

\(=12\)