\(\dfrac{7}{2}\) : \(\dfrac{2}{5}\) = x : \(\dfrac{8}{7}\)

x : \(\dfrac{8}{7}\) = \(\dfrac{7}{2}\) : \(\dfrac{2}{5}\)

x : \(\dfrac{8}{7}\) = \(\dfrac{35}{4}\)

x       = \(\dfrac{35}{4}\) . \(\dfrac{8}{7}\)

x = 10

10

\(\dfrac{7}{2}\)\(:\dfrac{2}{5}\)\(=x:\dfrac{8}{7}\)

\(\dfrac{35}{4}=x:\dfrac{8}{7}\)

\(x=\dfrac{35}{4}:\dfrac{8}{7}=\dfrac{245}{32}\)

Vậy \(x=\dfrac{245}{32}\)
 

a: \(0.4\cdot\sqrt{0.25-\sqrt{\dfrac{1}{4}}}=0.4\cdot\sqrt{0.25-0.5}\)(đề này sai rồi bạn)

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

\(\Leftrightarrow2\left(x-1\right)=\dfrac{-11}{2}-\dfrac{3}{2}=-7\)

\(\Leftrightarrow x-1=\dfrac{-7}{2}\)

hay \(x=-\dfrac{5}{2}\)

a, \(\dfrac{3}{7}\)\(x\) - 0,4 = - \(\dfrac{17}{35}\)

    \(\dfrac{3}{7}\)\(x\)         = - \(\dfrac{17}{35}\) + 0,4

     \(\dfrac{3}{7}\)\(x\)       = - \(\dfrac{3}{35}\)

        \(x\)       = - \(\dfrac{3}{35}\): \(\dfrac{3}{7}\)

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

b, 0,2.(\(x\) - 3) +2,4 = 10

    0,2.(\(x\) - 3)          = 10 - 2,4

    0,2.(\(x\) - 3)          = 7,6

           \(x\) - 3            = 7,6:0,2

           \(x\) - 3            = 38

            \(x\)                = 38 + 3

             \(x\)                = 41

\(\dfrac{3}{7}x-0,4=\dfrac{-17}{35}\)

\(\dfrac{3}{7}x=\dfrac{-17}{35}+0,4=\dfrac{-34}{70}+\dfrac{28}{70}\)

\(\dfrac{3}{7}x=\dfrac{-6}{70}=\dfrac{-3}{35}\)

\(x=\dfrac{-3}{35}:\dfrac{3}{7}=\dfrac{-3}{35}\cdot\dfrac{7}{3}\)

\(x=\dfrac{3\cdot\left(-1\right)\cdot7}{5\cdot7\cdot3}=-\dfrac{1}{5}\)

b) \(0,2\left(x-3\right)+2,4=10\)

\(0,2\left(x-3\right)=10-2,4=7,6\)

\(x-3=7,6:0,2=38\)

\(x=38+3=41\)

c) \(\left(x:2,2\right)\cdot\dfrac{1}{6}=\dfrac{-3}{8}\cdot\left(0,5-1\dfrac{3}{5}\right)\)

\(\left(x:2,2\right)\cdot\dfrac{1}{6}=\dfrac{-3}{8}\cdot\dfrac{-11}{10}\)

\(x:2,2=\dfrac{-3}{8}\cdot\dfrac{-11}{10}\cdot\dfrac{6}{1}\)

\(x:2,2=\dfrac{-3\cdot\left(-11\right)\cdot2\cdot3}{2\cdot4\cdot10\cdot1}=\dfrac{99}{40}\)

\(x=\dfrac{99}{40}\cdot2,2=\dfrac{99}{40}\cdot\dfrac{22}{10}\)

\(x=\dfrac{99\cdot2\cdot11}{40\cdot2\cdot5}=\dfrac{1089}{200}\)

 

 

\(M=\left(\dfrac{\dfrac{2}{5}-\dfrac{2}{9}+\dfrac{2}{11}}{\dfrac{7}{5}-\dfrac{7}{9}+\dfrac{7}{11}}-\dfrac{\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{5}}{\dfrac{7}{6}-\dfrac{7}{8}+\dfrac{7}{10}}\right)\times\dfrac{2022}{2021}\)

\(M=\left(\dfrac{\dfrac{178}{495}}{\dfrac{623}{495}}-\dfrac{\dfrac{17}{60}}{\dfrac{119}{120}}\right)\times\dfrac{2022}{2021}\)

\(M=\left(\dfrac{2}{7}-\dfrac{2}{7}\right)\times\dfrac{2022}{2021}\)

\(M=0\times\dfrac{2022}{2021}\)

M=0

\(a,0,5+\dfrac{1}{3}+0,4+\dfrac{5}{7}-\dfrac{1}{6}-\dfrac{4}{35}\\ =\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{2}{5}+\dfrac{5}{7}-\dfrac{1}{6}-\dfrac{4}{35}\\ =\dfrac{5}{6}+\dfrac{39}{35}-\dfrac{1}{6}-\dfrac{4}{35}\\ =\left(\dfrac{5}{6}-\dfrac{1}{6}\right)+\left(\dfrac{39}{35}-\dfrac{4}{35}\right)\\ =\dfrac{2}{3}+1\\ =\dfrac{4}{3}.\)

\(b,\left(3-\dfrac{1}{4}+\dfrac{2}{3}\right)-\left(5+\dfrac{1}{3}-\dfrac{6}{5}\right)-\left(-6-\dfrac{7}{4}+\dfrac{3}{2}\right)\\ =3-\dfrac{1}{4}+\dfrac{2}{3}-5-\dfrac{1}{3}+\dfrac{6}{5}+6+\dfrac{7}{4}-\dfrac{3}{2}\\ =\left(3-5+6\right)+\left(-\dfrac{1}{4}+\dfrac{7}{4}\right)+\left(\dfrac{2}{3}-\dfrac{1}{3}\right)+\left(\dfrac{6}{5}+\dfrac{7}{4}\right)\\ =4-\dfrac{3}{2}+\dfrac{1}{3}+\dfrac{59}{20}\\ =\dfrac{5}{2}+\dfrac{1}{3}+\dfrac{59}{20}\\ =\dfrac{17}{6}+\dfrac{59}{20}\\ =\dfrac{347}{60}.\)

\(c,\dfrac{1}{3}-\dfrac{3}{4}-\left(-\dfrac{3}{5}\right)+\dfrac{1}{64}-\dfrac{2}{9}-\dfrac{1}{36}+\dfrac{1}{15}\\ =\dfrac{1}{3}+\dfrac{3}{4}+\dfrac{3}{5}+\dfrac{1}{64}-\dfrac{2}{9}-\dfrac{1}{36}+\dfrac{1}{15}\\ =\left(\dfrac{1}{3}-\dfrac{2}{9}\right)+\left(\dfrac{3}{4}-\dfrac{1}{36}\right)+\left(\dfrac{3}{5}+\dfrac{1}{15}\right)+\dfrac{1}{64}\\ =\dfrac{1}{9}+\dfrac{13}{18}+\dfrac{2}{3}+\dfrac{1}{64}\\ =\dfrac{3}{2}+\dfrac{1}{64}\\ =\dfrac{65}{64}.\)

\(\dfrac{0,4-\dfrac{2}{9}+\dfrac{2}{11}}{1,4-\dfrac{7}{9}+\dfrac{7}{11}}-\dfrac{\dfrac{1}{3}-0,25+\dfrac{1}{5}}{1\dfrac{1}{6}-0,875+0,7}\\ =\dfrac{2\left(0,2-\dfrac{1}{9}+\dfrac{1}{11}\right)}{7\left(0,2-\dfrac{1}{9}+\dfrac{1}{11}\right)}-\dfrac{2\left(\dfrac{1}{6}-0,125+0,1\right)}{7\left(\dfrac{1}{6}-0,125+0,1\right)}\\ =\dfrac{2}{7}-\dfrac{2}{7}\\ =0\)

\(A=\left(3-\dfrac{1}{4}+\dfrac{3}{2}\right)-\left(5+\dfrac{1}{3}-\dfrac{5}{6}\right)-\left(6-\dfrac{7}{4}+\dfrac{2}{3}\right)\\ \Rightarrow A=3-\dfrac{1}{4}+\dfrac{3}{2}-5-\dfrac{1}{3}+\dfrac{5}{6}-6+\dfrac{7}{4}-\dfrac{2}{3}\\ \Rightarrow A=\left(3-5-6\right)-\left(\dfrac{1}{4}+\dfrac{7}{4}\right)+\left(\dfrac{3}{2}+\dfrac{5}{6}-\dfrac{2}{3}\right)\\ \Rightarrow A=-8-\dfrac{3}{2}+\dfrac{5}{3}\\ =-\dfrac{47}{6}.\\ B=0,5+\dfrac{1}{3}+0,4+\dfrac{5}{7}+\dfrac{1}{6}-\dfrac{4}{35}+\dfrac{1}{41}\)

\(\Rightarrow B=\left(0,5+0,4\right)+\left(\dfrac{1}{3}+\dfrac{1}{6}\right)+\left(\dfrac{5}{7}-\dfrac{4}{35}\right)+\dfrac{1}{41}\\ \Rightarrow B=\dfrac{9}{10}+\dfrac{1}{2}+\dfrac{3}{5}+\dfrac{1}{41}\\ \Rightarrow B=2+\dfrac{1}{41}\\ \Rightarrow B=\dfrac{83}{41}.\)

-_-

A=(3− 

4

1

​

 + 

2

3

​

 )−(5+ 

3

1

​

 − 

6

5

​

 )−(6− 

4

7

​

 + 

3

2

​

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⇒A=3− 

4

1

​

 + 

2

3

​

 −5− 

3

1

​

 + 

6

5

​

 −6+ 

4

7

​

 − 

3

2

​

 

⇒A=(3−5−6)−( 

4

1

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 + 

4

7

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 )+( 

2

3

​

 + 

6

5

​

 − 

3

2

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⇒A=−8− 

2

3

​

 + 

3

5

​

 

=− 

6

47

​

 .

B=0,5+ 

3

1

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7

5

​

 + 

6

1

​

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35

4

​

 + 

41

1

​

 

 

\Rightarrow B=\left(0,5+0,4\right)+\left(\dfrac{1}{3}+\dfrac{1}{6}\right)+\left(\dfrac{5}{7}-\dfrac{4}{35}\right)+\dfrac{1}{41}\\ \Rightarrow B=\dfrac{9}{10}+\dfrac{1}{2}+\dfrac{3}{5}+\dfrac{1}{41}\\ \Rightarrow B=2+\dfrac{1}{41}\\ \Rightarrow B=\dfrac{83}{41}.⇒B=(0,5+0,4)+( 

3

1

​

 + 

6

1

​

 )+( 

7

5

​

 − 

35

4

​

 )+ 

41

1

​

 

⇒B= 

10

9

​

 + 

2

1

​

 + 

5

3

​

 + 

41

1

​

 

⇒B=2+ 

41

1

​

 

⇒B= 

41

83

​

 .

\(B=\left(1,6\cdot0,4\right)^2-\dfrac{57}{4}+\dfrac{7}{5}-\dfrac{7}{4}=\dfrac{256}{625}-16+\dfrac{7}{5}=-\dfrac{8869}{625}\)

\(M=\left(\dfrac{0,4-\dfrac{2}{9}+\dfrac{2}{11}}{1,4-\dfrac{7}{9}+\dfrac{7}{11}}-\dfrac{\dfrac{1}{3}-0,25+\dfrac{1}{5}}{1\dfrac{1}{6}-0,875+0,7}\right):\dfrac{2012}{2013}\)

\(M=\left(\dfrac{\dfrac{2}{5}-\dfrac{2}{9}+\dfrac{2}{11}}{\dfrac{7}{5}-\dfrac{7}{9}+\dfrac{7}{11}}-\dfrac{\dfrac{2}{6}-\dfrac{2}{8}+\dfrac{2}{10}}{\dfrac{7}{6}-\dfrac{7}{8}+\dfrac{7}{10}}\right):\dfrac{2012}{2013}\)

\(M=\left(\dfrac{2\left(\dfrac{1}{5}-\dfrac{1}{9}+\dfrac{1}{11}\right)}{7\left(\dfrac{1}{5}-\dfrac{1}{9}+\dfrac{1}{11}\right)}-\dfrac{2\left(\dfrac{1}{6}-\dfrac{1}{8}+\dfrac{1}{10}\right)}{7\left(\dfrac{1}{6}-\dfrac{1}{8}+\dfrac{1}{10}\right)}\right):\dfrac{2012}{2013}\)

\(M=\left(\dfrac{2}{7}-\dfrac{2}{7}\right).\dfrac{2013}{2012}\)

\(M=0.\dfrac{2013}{2012}\)

\(M=0\)