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Bài 1: 

a: \(A=\dfrac{1\left(\dfrac{1}{13}-\dfrac{1}{17}-\dfrac{1}{23}\right)}{2\left(\dfrac{1}{13}-\dfrac{1}{17}-\dfrac{1}{23}\right)}\cdot\dfrac{\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{5}}{\dfrac{7}{6}-\dfrac{7}{8}+\dfrac{7}{10}}+\dfrac{6}{7}\)

\(=\dfrac{1}{2}\cdot\dfrac{2}{7}+\dfrac{6}{7}=\dfrac{1}{7}+\dfrac{6}{7}=1\)

b: \(B=2000:\left[\dfrac{\dfrac{2}{5}-\dfrac{2}{9}+\dfrac{2}{11}}{\dfrac{7}{5}-\dfrac{7}{9}+\dfrac{7}{11}}\cdot\dfrac{-\dfrac{7}{6}+\dfrac{7}{8}-\dfrac{7}{10}}{\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{5}}\right]\)

\(=2000:\left[\dfrac{2}{7}\cdot\dfrac{-7}{2}\right]=-2000\)

c: \(C=10101\cdot\left(\dfrac{5}{111111}+\dfrac{1}{111111}-\dfrac{4}{111111}\right)\)

\(=10101\cdot\dfrac{2}{111111}=\dfrac{2}{11}\)

2 tháng 4 2017

1. Tìm \(x\):

a) \(\dfrac{x}{5}=\dfrac{5}{6}+\dfrac{-19}{30}\)

\(\dfrac{x}{5}=\dfrac{1}{5}\)

\(\Rightarrow x=1\)

b) \(\dfrac{-5}{6}-x=\dfrac{7}{12}-\dfrac{1}{3}.x\)

\(\dfrac{-5}{6}-\dfrac{7}{12}=x-\dfrac{1}{3}.x\)

\(x-\dfrac{1}{3}.x=\dfrac{-17}{12}\)

\(\dfrac{2}{3}.x=\dfrac{-17}{12}\)

\(x=\dfrac{-17}{12}:\dfrac{2}{3}\)

\(x=\dfrac{-17}{8}\)

c) \(2016^3.2016^x=2016^8\)

\(2016^x=2016^8:2016^3\)

\(2016^x=2016^{8-3}\)

\(2016^x=2016^5\)

\(\Rightarrow x=5\)

d) \(\left(x+\dfrac{3}{4}\right):\dfrac{5}{2}=3\dfrac{1}{2}\)

\(\left(x+\dfrac{3}{4}\right):\dfrac{5}{2}=\dfrac{7}{2}\)

\(\left(x+\dfrac{3}{4}\right)=\dfrac{7}{2}.\dfrac{5}{2}\)

\(x+\dfrac{3}{4}=\dfrac{35}{4}\)

\(x=\dfrac{35}{4}-\dfrac{3}{4}\)

\(x=\dfrac{32}{4}=8\)

e) \(\left(2,8.x-2^5\right):\dfrac{2}{3}=3^2\)

\(\left(2,8.x-2^5\right)=9.\dfrac{2}{3}\)

\(2,8.x-2^5=6\)

\(2,8.x=6+32\)

\(2,8.x=38\)

\(x=38:2,8\)

\(x=\dfrac{95}{7}\)

f) \(\dfrac{4}{7}.x-\dfrac{2}{3}=\dfrac{2}{5}\)

\(\dfrac{4}{7}.x=\dfrac{2}{5}+\dfrac{2}{3}\)

\(\dfrac{4}{7}.x=\dfrac{16}{15}\)

\(x=\dfrac{16}{15}:\dfrac{4}{7}\)

\(x=\dfrac{28}{15}\)

g) \(\left(\dfrac{3x}{7}+1\right):\left(-4\right)=\dfrac{-1}{28}\)

\(\left(\dfrac{3x}{7}+1\right)=\dfrac{-1}{28}.\left(-4\right)\)

\(\dfrac{3x}{7}+1=\dfrac{1}{7}\)

\(\dfrac{3x}{7}=\dfrac{1}{7}-1\)

\(\dfrac{3x}{7}=\dfrac{-6}{7}\)

\(\Rightarrow3x=-6\)

\(x=\left(-6\right):3\)

\(x=-2\)

2 tháng 4 2017

2. Thực hiện phép tính:

a) \(\dfrac{1}{2}+\dfrac{1}{2}.\dfrac{2}{3}-\dfrac{1}{3}:\dfrac{3}{4}+1\dfrac{4}{5}\)

\(=\dfrac{1}{2}.\left(\dfrac{2}{3}+1\right)-\dfrac{1}{3}:\dfrac{3}{4}+\dfrac{9}{5}\)

\(=\dfrac{1}{2}.\dfrac{5}{3}-\dfrac{1}{3}:\dfrac{3}{4}+\dfrac{9}{5}\)

\(=\dfrac{5}{6}-\dfrac{4}{9}+\dfrac{9}{5}\)

\(=\dfrac{7}{18}+\dfrac{9}{5}\)

\(=\dfrac{197}{90}\)

b) \(\dfrac{7.5^2-7^2}{7.24+21}\)

\(=\dfrac{7.25-7.7}{7.24+7.3}\)

\(=\dfrac{7.\left(25-7\right)}{7.\left(24+3\right)}\)

\(=\dfrac{7.18}{7.27}\)

\(=\dfrac{2}{3}\)

c) \(\dfrac{2}{3}+\dfrac{1}{3}.\left(\dfrac{-4}{9}+\dfrac{5}{6}\right):\dfrac{7}{12}\)

\(=\dfrac{2}{3}+\dfrac{1}{3}.\dfrac{7}{18}:\dfrac{7}{12}\)

\(=\dfrac{2}{3}+\dfrac{7}{54}:\dfrac{7}{12}\)

\(=\dfrac{2}{3}+\dfrac{2}{9}\)

\(=\dfrac{8}{9}\)

12 tháng 8 2017

a)\(\dfrac{2}{3}-\dfrac{3}{5}:\left(-1\dfrac{1}{5}\right)+\left(\dfrac{-2}{3}\right)\cdot\dfrac{3}{8}\)

\(=\dfrac{2}{3}-\dfrac{3}{5}\cdot\dfrac{-5}{6}+\left(\dfrac{-1}{4}\right)=\dfrac{5}{12}+\dfrac{1}{2}=\dfrac{11}{12}\)

b)\(17\dfrac{11}{9}-\left(6\dfrac{3}{13}+7\dfrac{11}{19}\right)+\left(10\dfrac{3}{13}-5\dfrac{1}{4}\right)=\dfrac{164}{9}-\left(\dfrac{81}{13}+\dfrac{144}{19}\right)+\left(\dfrac{133}{13}-\dfrac{21}{4}\right)=\dfrac{164}{9}-\dfrac{3411}{247}+\dfrac{259}{52}=\dfrac{6425}{684}\)

c)\(\left(\dfrac{-3}{2}\right)^2-\left[-2\dfrac{1}{3}-\left(\dfrac{3}{4}+\dfrac{1}{3}\right):2\dfrac{3}{5}\right]\cdot\left(\dfrac{-3}{4}\right)=\dfrac{9}{4}-\left[\dfrac{-7}{3}-\dfrac{13}{12}\cdot\dfrac{5}{13}\right]\cdot\left(\dfrac{-3}{4}\right)=\dfrac{9}{4}-\left(\dfrac{-11}{4}\right)\cdot\left(\dfrac{-3}{4}\right)=\dfrac{3}{16}\)

d)\(\dfrac{21}{33}:\dfrac{11}{5}-\dfrac{13}{33}:\dfrac{11}{5}+\dfrac{25}{33}:\dfrac{11}{5}+\dfrac{6}{11}=\dfrac{5}{11}\cdot\left(\dfrac{21}{33}-\dfrac{13}{33}+\dfrac{25}{33}\right)+\dfrac{6}{11}=\dfrac{5}{11}\cdot1+\dfrac{6}{11}=1\)

12 tháng 8 2017

\(a)\dfrac{2}{3}-\dfrac{3}{5}:\left(-1\dfrac{1}{5}\right)+\left(\dfrac{-2}{3}\right).\dfrac{3}{8}\)

\(=\dfrac{2}{3}-\dfrac{3}{5}:\left(\dfrac{-6}{5}\right)+\left(\dfrac{-2}{3}\right).\dfrac{3}{8}\)

\(=\dfrac{2}{3}-\dfrac{-1}{2}+\left(\dfrac{-2}{3}\right).\dfrac{3}{8}\)

\(=\dfrac{2}{3}-\dfrac{-1}{2}+\dfrac{-1}{4}\)

\(=\dfrac{7}{6}+\dfrac{-1}{4}\)

\(=\dfrac{11}{12}\)

27 tháng 3 2017

A=\(\dfrac{2}{7}+\dfrac{-3}{8}+\dfrac{11}{7}+\dfrac{1}{3}+\dfrac{1}{7}+\dfrac{5}{-3}\)

A=\(\left(\dfrac{2}{7}+\dfrac{11}{7}+\dfrac{1}{7}\right)+\left(\dfrac{1}{3}+\dfrac{5}{-3}\right)+\dfrac{-3}{8}\)

A=\(2+\dfrac{-4}{3}+\dfrac{-3}{8}\)

A=\(\dfrac{7}{24}\)

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

B=\(\left(\dfrac{3}{17}+\dfrac{14}{17}\right)+\left(\dfrac{-18}{35}+\dfrac{17}{-35}\right)+\left(\dfrac{-5}{13}+\dfrac{-8}{13}\right)\)

B=\(\dfrac{17}{17}+\dfrac{-35}{35}+\dfrac{-13}{13}\)

B=\(1+\left(-1\right)+\left(-1\right)=-1\)

C=\(\dfrac{-3}{17}+\left(\dfrac{2}{3}+\dfrac{3}{17}\right)\)

C=\(\dfrac{-3}{17}+\dfrac{2}{3}+\dfrac{3}{17}=\left(\dfrac{-3}{17}+\dfrac{3}{17}\right)+\dfrac{2}{3}\)

C=0+\(\dfrac{2}{3}=\dfrac{2}{3}\)

D=\(\left(\dfrac{-1}{6}+\dfrac{5}{-12}\right)+\dfrac{7}{12}\)

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

D=\(\dfrac{-2}{12}+\dfrac{-5}{12}+\dfrac{7}{12}=\left(\dfrac{-2}{12}+\dfrac{-5}{12}\right)+\dfrac{7}{12}\)

D=\(\dfrac{-7}{12}+\dfrac{7}{12}=0\)

16 tháng 3 2018

a, Ta có :

\(\dfrac{1}{6}< \dfrac{1}{5}\)

\(\dfrac{1}{7}< \dfrac{1}{5}\)

.................

\(\dfrac{1}{9}< \dfrac{1}{5}\)

\(\dfrac{1}{10}=\dfrac{1}{10}\)

\(\dfrac{1}{11}< \dfrac{1}{10}\)

..................

\(\dfrac{1}{17}< \dfrac{1}{10}\)

\(\Leftrightarrow\dfrac{1}{5}+\dfrac{1}{6}+\dfrac{1}{7}+......+\dfrac{1}{17}< \dfrac{1}{5}+\dfrac{1}{5}+....+\dfrac{1}{5}\)

\(\Leftrightarrow A< \dfrac{1}{5}.5+\dfrac{1}{10}.8\)

\(\Leftrightarrow A< 1+\dfrac{4}{5}=\dfrac{9}{5}< 2\)

\(\Leftrightarrow A< 2\left(đpcm\right)\)

b/ Ta có :

\(\dfrac{1}{11}>\dfrac{1}{30}\)

\(\dfrac{1}{12}>\dfrac{1}{30}\)

...............

\(\dfrac{1}{29}>\dfrac{1}{30}\)

\(\dfrac{1}{30}=\dfrac{1}{30}\)

\(\Leftrightarrow\dfrac{1}{11}+\dfrac{1}{12}+........+\dfrac{1}{30}>\dfrac{1}{30}+\dfrac{1}{30}+.......+\dfrac{1}{30}\)

\(\Leftrightarrow B>\dfrac{1}{30}.20=\dfrac{2}{3}\)

\(\Leftrightarrow B>\dfrac{2}{3}\left(đpcm\right)\)

1 tháng 5 2017

Đổi hết ra số thập phân mà so sánh ý bạn.

1 tháng 5 2017

Vậy bạn đổi và làm giúp mình với

9 tháng 4 2017

a) \(\dfrac{37}{40}-0,64\\ =\dfrac{37}{40}-\dfrac{16}{25}\\ =\dfrac{185}{200}-\dfrac{128}{200}\\ =\dfrac{57}{200}\)

9 tháng 4 2017

b) \(130\dfrac{25}{28}-120\dfrac{12}{35}\\ =\dfrac{3665}{28}-\dfrac{4212}{35}\\ =\dfrac{18325}{140}-\dfrac{16848}{140}\\ =\dfrac{211}{20}\)

8 tháng 5 2017

1,

x =( -12 . ( -3) ) : 2

x = 18

2,

a, -7/9 . 6/11 + (-2/9) = -14/33 + (-2/9) = -64/99

b, -4/7 : 2 = -4/7 . 1/2 = -2/7

c, 115 - (24 - 5. 3) = 115 - ( 24 - 15) = 115 - 9 = 106

d,= -3/7. (5/9 + 4/9) + 17/7 = -3/7 . 1 +17/7 = -3/7 . 17/7 = -51/49

e, ??? mình cx k biếtleuleu

8 tháng 5 2017

Lời giải:

\(\dfrac{x}{-12}=\dfrac{-3}{2}\)

\(\Rightarrow2x=-12.\left(-3\right)\)

\(\Rightarrow2x=36\)

\(\Rightarrow x=18\)

23 tháng 7 2017

Các bạn không cần trả lời câu hỏi trên của mik vì mik đã hiểu rồi nha . Cho nên đừng trả lời ! OKleuleu

23 tháng 7 2017

Mình khuyen bạn phải suy nghĩ kĩ bài trước khi đăng lên nhé!!hum