Câu a:

\(\frac27\) + \(\frac{-3}{8}\) + \(\frac{11}{7}\) + \(\frac17\) + \(\frac{5}{-8}\)

= (\(\frac27+\frac{11}{7}+\frac17\)) -(\(\frac38\) + \(\frac58\))

= (\(\frac{13}{7}+\frac17\)) - \(\frac88\)

= \(\frac{14}{7}-1\)

= 2 - 1

= 1

Câu b:

\(\frac{3}{17}+\frac{-5}{13}+\frac{-18}{35}+\frac{14}{17}+\frac{17}{-35}+\frac{-8}{13}\)

= (\(\frac{3}{17}+\frac{14}{17}\)) - (\(\frac{5}{13}\) + \(\frac{8}{13}\)) - (\(\frac{18}{35}+\frac{17}{35}\))

= \(\frac{17}{17}-\frac{18}{18}-\) \(\frac{35}{35}\)

= 1 - 1 - 1

= 0 - 1

= -1

bài 1) a) \(1+2+3+4+........+2005+2006\)

\(\Leftrightarrow\) \(\left(1+2006\right)+\left(2+2005\right)+........+\left(1003+1004\right)\)

\(\Leftrightarrow\) \(2007.\dfrac{2006}{2}=2007.1003=2013021\)

b) \(5+10+15+.......+2000+2005\)

\(\Leftrightarrow\) \(\left(2005+5\right)\left(2000+10\right)+.......+\left(1000+1010\right)\)

\(\Leftrightarrow\) \(2010.\dfrac{2005}{5}=2010.401=405010\)

c) \(140+136+132+.......+64+60\)

\(\Leftrightarrow\) \(\left(140+60\right)+\left(136+64\right)+.......+\left(100+100\right)\)

\(\Leftrightarrow\) \(200.10\) = \(2000\)

1)

a) \(1+2+3+4+.....+2005+2006\)

Số các số hạng của dãy trên là:

\((2006-1):1+1=2006\)

Tổng dãy là:

\(\dfrac{2006\left(2006+1\right)}{2}=2013021\)

b) \(5+10+15+.....+2000+2005\)

Số các số hạng của dãy là:

\((2005-5):5+1=401\)

Tổng dãy là:

\(\dfrac{401\left(2005+5\right)}{2}=403005\)

c)\(140+136+132+.....+64+60\)

\(=60+64+.....+132+136+140\)

Số số hạng của dãy là:

\((140-60):4+1=11\)

Tổng dãy là:

\(\dfrac{11\left(60+140\right)}{2}=1100\)

Tính các tổng dưới đây sau khi đã rút gọn phân số :

a)\(\dfrac{7}{21}\) + \(\dfrac{9}{-36}\) = \(\dfrac{7}{21}\)+\(\dfrac{-9}{36}\)=\(\dfrac{1}{3}\)+\(\dfrac{-1}{4}\)=\(\dfrac{4}{12}\)+\(\dfrac{-3}{12}\)=\(\dfrac{1}{12}\)

b) \(\dfrac{-12}{18}\)+\(\dfrac{-21}{35}\)=\(\dfrac{-2}{3}\)+\(\dfrac{-3}{5}\)=\(\dfrac{-10}{15}\)+\(\dfrac{-9}{15}\)=\(\dfrac{-19}{15}\)

c) \(\dfrac{-3}{21}\)+\(\dfrac{6}{42}\)=\(\dfrac{-1}{7}\)+\(\dfrac{1}{7}\)=0

d) \(\dfrac{-18}{24}\)+\(\dfrac{15}{-21}\)=\(\dfrac{-18}{24}\)+\(\dfrac{-15}{21}\)=\(\dfrac{-3}{4}\)+\(\dfrac{-5}{7}\)=\(\dfrac{-21}{28}\)+\(\dfrac{-20}{28}\)=\(\dfrac{-41}{28}\)

a) 25⁵⁰.125⁵
= (5²)⁵⁰.(5³)⁵
= 5¹⁰⁰.5¹⁵
= 5¹⁰⁰⁺¹⁵
= 5¹¹⁵
b) 9²⁵.27⁴.81³
= (3²)²⁵.(3³)⁴.(3⁴)³
= 3⁵⁰.3¹².3¹²
= 3^50+12+12
= 3⁷⁴
d) 12⁷:6⁷
= (12:6)⁷
= 2⁷
 

a, x+7=12

x=12-7

x=5

b, x-15=-21

x=-21+15

x=-6

c, 17-(x-9)=12

x-9=17-12

x-9=5

x=5+9

x=14

d, \(\left|x\right|+\left|-35\right|=41\)

\(\left|x\right|+35=41\)

\(\left|x\right|=41-35\)

\(\left|x\right|=6\)

\(\Rightarrow x=6\) hoặc \(x=-6\)

Vậy \(x\in\left\{6;-6\right\}\)

e, \(\left|x+3\right|=6\)

=> x+3=6 hoặc x+3=-6

+) x+3=6

x=6-3

x=3

+) x+3=-6

x=(-6)-3

x=-3

f, \(\left|-11\right|-\left|2-x\right|=9\)

\(11-\left|2-x\right|=9\)

\(\left|2-x\right|=11-9\)

\(\left|2-x\right|=2\)

\(\Rightarrow2-x=2\) hoặc \(2-x=-2\)

+) 2-x=2

x=2-2=0

+) 2-x=-2

x=2-(-2)=4

Thanks nhiều nha Nguyễn Quỳnh Chi

a) 15 . 2³ + 4. 2³ - 5.7

= 15 . 8 + 4.8 - 35

= 120 + 32 - 35

= 152 - 35

= 117

b) 49 . 213+ 87. 7²

=49.213+ 87. 49

=10437 + 4263

= 14700

c) 20+21+22+23+24+25+26+27+28+29+30

d) 5⁶ : 5³ + 3 . 3²

= 5⁶ : 5³ + 3. 9

=5³ + 27

= 125+ 27

= 152

e) 2 . 325 . 12 + 4 . 69 . 24 + 3 . 399 . 8

= 7800+ (6624+ 9576)

=7800+ 16200

= 24000

thank you very much

a) \(\frac{-28}{19}\). \(\frac{\left(-38\right)}{14}\)= 4

b) \(\frac{-21}{16}\). \(\frac{\left(-24\right)}{7}\)= \(\frac{9}{2}\)

c) \(\frac{12}{17}\). \(\frac{\left(-34\right)}{9}\)= \(\frac{-8}{3}\)

d) \(\frac{\left(-15\right)}{4}\): \(\frac{21}{10}\)= \(\frac{-25}{14}\)

e) \(-2\frac{1}{7}\): \(-1\frac{1}{14}\)= 2

nhớ ủng hộ mik nha mn

a.=4

b.=119/24

c.= -8/3

d.= -25/14

Mình chỉ làm đc từng này thôi

b1: a, 6¹².(15+19-34)=6¹².0=0

b,4¹⁴.(37.4+23.4-240)=4¹⁴.0=0

c,(5¹⁷.125-5¹⁸.25)+6³:2³=(5¹⁷.5³-5¹⁸.5²)+3³=0+27=27

b2:a,143+7.(n-17)=206

===> 7.(n-17)=206-143=63

====>n-17=63:7=9

=====>n=9+17=26

vậy n=26

b,128-28:(15-n)=124

====>28:(15-n)=128-124=4

=====> 15-n=28:4=7

=====> n=15-7=8

vậy n=8

c,3ⁿ.2+48=210

====>3ⁿ.2=210-48=162

====>3ⁿ=162:2=81=3⁴

====>n=4

vậy n=4