\(\dfrac{8}{7}:\left(\dfrac{2}{9}-\dfrac{1}{18}\right)+\dfrac{7}{8}:\left(\dfrac{1}{36}-\dfrac{5}{12}\right)\)

\(=\dfrac{8}{7}:\left(\dfrac{4}{18}-\dfrac{1}{18}\right)+\dfrac{7}{8}:\left(\dfrac{1}{36}-\dfrac{15}{36}\right)\)

\(=\dfrac{8}{7}:\dfrac{1}{6}+\dfrac{7}{8}:\dfrac{-7}{18}\)

\(=\dfrac{8}{7}.6+\dfrac{7}{8}.\dfrac{-18}{7}\)

\(=\dfrac{129}{28}\)

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

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

\(\dfrac{-18}{14}+\dfrac{15}{-21}=\dfrac{-9}{7}+\dfrac{-5}{7}=\dfrac{-14}{7}=-2\)

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

lỗi

x + 4/9 + 8/18 + 12/27 + 16/36 = 16/9

 x + (4/9+12/27)+(8/12+16/36) = 16/9

 x +       8/9         +     10/9        = 16/9

  x +               2                         = 16/9

  x                                              = 16/9 - 2

  x                                               =  -2/18  

x+4/9+4/9+4/9+4/9=16/9
x+4/9.4=16/9
x+16/9=16/9
-->    x = 0

Câu 1:

\(-\dfrac{5}{7}\cdot\dfrac{7}{-45}=\dfrac{1}{9}\) ; \(-\dfrac{3}{10}\cdot-30=9\) ; \(-12\cdot-\dfrac{2}{36}=\dfrac{2}{3}\)

Caau2;3;4;5,... tự bấm máy tính là ra

\(=\dfrac{7}{8}\left(\dfrac{2}{9}-\dfrac{1}{18}+\dfrac{1}{36}-\dfrac{5}{12}\right)=\dfrac{7}{8}\cdot\dfrac{8-2+1-15}{36}\)

\(=\dfrac{7}{8}\cdot\dfrac{-8}{36}=\dfrac{-7}{36}\)

\(\dfrac{24}{54}\)

các phân số bằng \(\dfrac{4}{9}\)là

\(\dfrac{24}{54}\)

\(\dfrac{24}{54}\)

\(\dfrac{7}{8}\): \(\left(\dfrac{2}{9}-\dfrac{1}{18}\right)\)+\(\dfrac{7}{8}\): \(\left(\dfrac{1}{36}-\dfrac{5}{12}\right)\)

= \(\dfrac{7}{8}\): \(\dfrac{1}{6}\)+\(\dfrac{7}{8}\): \(\left(\dfrac{-14}{36}\right)\)

= \(\dfrac{7}{8}\): \(\left\{\dfrac{1}{6}+\left(\dfrac{-14}{36}\right)\right\}\)

= \(\dfrac{7}{8}\): \(\left(\dfrac{-2}{9}\right)\)

= \(\dfrac{7}{8}\). \(\left(\dfrac{-9}{2}\right)\)

= \(\dfrac{-63}{16}\)

Giải:

\(\dfrac{7}{8}:\left(\dfrac{2}{9}-\dfrac{1}{18}\right)+\dfrac{7}{8}:\left(\dfrac{1}{36}-\dfrac{5}{12}\right)\)

\(=\dfrac{7}{8}:\left(\dfrac{4}{18}-\dfrac{1}{18}\right)+\dfrac{7}{8}:\left(\dfrac{1}{36}-\dfrac{15}{36}\right)\)

\(=\dfrac{7}{8}:\dfrac{3}{18}+\dfrac{7}{8}:\left(-\dfrac{7}{18}\right)\)

\(=\dfrac{7}{8}.6+\dfrac{7}{8}.\dfrac{18}{-7}\)

\(=\dfrac{7}{8}\left(6+\dfrac{18}{-7}\right)\)

\(=\dfrac{7}{8}.\dfrac{24}{7}\)

\(=3\)

Vậy giá trị của biểu thức trên là 3.

Chúc bạn học tốt!!!

\(\dfrac{7}{8}:\left(\dfrac{2}{9}-\dfrac{1}{18}\right)+\dfrac{7}{8}:\left(\dfrac{1}{36}-\dfrac{5}{12}\right)\)

\(=\dfrac{7}{8}:\left(\dfrac{4}{18}-\dfrac{1}{18}\right)+\dfrac{7}{8}:\left(\dfrac{1}{36}-\dfrac{15}{36}\right)\)

\(=\dfrac{7}{8}:\dfrac{3}{18}+\dfrac{7}{8}:\left(\dfrac{-7}{18}\right)\)

\(=\dfrac{7}{8}.6+\dfrac{7}{8}.\dfrac{-18}{7}\)

\(=\dfrac{7}{8}.\left(6+\dfrac{-18}{7}\right)\)

\(=\dfrac{7}{8}.\dfrac{24}{7}\)

\(=3\)

a: \(=\dfrac{13\left(3-18\right)}{40\left(15-2\right)}=\dfrac{13}{15-2}\cdot\dfrac{-15}{40}=\dfrac{-3}{8}\)

b: \(=\dfrac{18\left(34-124\right)}{36\left(-17-13\right)}=\dfrac{1}{2}\cdot\dfrac{-90}{-30}=\dfrac{3}{2}\)

c: \(=\dfrac{3\left(\dfrac{1}{41}-\dfrac{4}{47}+\dfrac{9}{53}\right)}{4\left(\dfrac{1}{41}-\dfrac{4}{47}+\dfrac{9}{53}\right)}+\dfrac{\dfrac{-1}{4}\cdot\dfrac{-2}{3}-\dfrac{3}{4}:\dfrac{1}{6}}{\dfrac{3}{2}\cdot\left(\dfrac{-2}{3}-\dfrac{3}{4}\cdot\dfrac{-2}{3}\right)}\)

\(=\dfrac{3}{4}+\dfrac{\dfrac{2}{12}-\dfrac{9}{2}}{\dfrac{3}{2}\cdot\dfrac{-1}{6}}=\dfrac{3}{4}+\dfrac{-13}{3}:\dfrac{-3}{12}=\dfrac{3}{4}+\dfrac{13}{3}\cdot\dfrac{12}{3}\)

\(=\dfrac{3}{4}+\dfrac{156}{9}=\dfrac{217}{12}\)

\(a)\dfrac{-11}{12}và\dfrac{17}{-18}\) \(\Leftrightarrow\dfrac{-11}{12}và\dfrac{-17}{18}\) \(\Leftrightarrow\dfrac{-33}{36}và\dfrac{-34}{36}\) 

Ta thấy rằng :  \(-33>-34\Rightarrow\dfrac{-33}{36}>\dfrac{-34}{36}\)

Hay : \(\dfrac{-11}{12}>\dfrac{17}{-18}\)

\(b)\dfrac{-14}{-21}và\dfrac{-60}{-72}\)

Ta có : \(\dfrac{-14}{-21}\text{=}\dfrac{-14:-7}{-21:-7}\text{=}\dfrac{2}{3}\text{=}\dfrac{4}{6}\)

\(\dfrac{-60}{-72}\text{=}\dfrac{-60:-12}{-72:-12}=\dfrac{5}{6}\)

Do đó : \(\dfrac{-14}{-21}< \dfrac{-60}{-72}\)

\(c)\dfrac{2135}{13790}và\dfrac{4}{3}\)

Xét phân số : \(\dfrac{2135}{13790}\) ta thấy rằng : \(tử< mẫu\left(2135< 13790\right)\)

\(\Rightarrow\dfrac{2135}{13790}< 1\)

Xét phân số : \(\dfrac{4}{3}có\) : \(tử>mẫu\left(4>3\right)\)

\(\Rightarrow\dfrac{4}{3}>1\)

Do đó : \(\dfrac{2135}{13790}< \dfrac{4}{3}\)

\(d)\dfrac{2022}{2021}và\dfrac{10}{9}\) 

Ta thấy rằng : \(\dfrac{2022}{2021}-\dfrac{1}{2021}\text{=}1\)

\(\dfrac{10}{9}-\dfrac{1}{9}\text{=}1\)

Mà : \(\dfrac{1}{9}>\dfrac{1}{2021}\)

\(\Rightarrow\dfrac{2022}{2021}< \dfrac{10}{9}\)

\(e)\dfrac{35}{36}và\dfrac{16}{17}\)

Ta có : \(\dfrac{35}{36}+\dfrac{1}{36}\text{=}1\)

            \(\dfrac{16}{17}+\dfrac{1}{17}\text{=}1\)

Mà : \(\dfrac{1}{36}< \dfrac{1}{17}\)

\(\Rightarrow\dfrac{35}{36}>\dfrac{16}{17}\)

\(f)-1,3< -1,2\)

a) Ta có: 

\(-\dfrac{11}{12}=\dfrac{1}{12}-1\)

\(-\dfrac{17}{18}=\dfrac{1}{18}-1\)

Mà: \(\dfrac{1}{12}>\dfrac{1}{18}\)

Hay: \(\dfrac{1}{12}-1>\dfrac{1}{18}-1\Rightarrow-\dfrac{11}{12}>-\dfrac{17}{18}\)

b) Ta có: 

\(\dfrac{-14}{-21}=\dfrac{2}{3}=\dfrac{4}{6}\)

\(\dfrac{-60}{-72}=\dfrac{5}{6}\)

Mà: \(5>4\Rightarrow\dfrac{-60}{-72}>\dfrac{-14}{-21}\)

c) Ta có:

\(\dfrac{2135}{13790}=\dfrac{61}{394}< 1\) (tử nhỏ hơn mẫu) 

\(\dfrac{4}{3}>1\) (tử lớn hơn mẫu) 

Ta có: \(\dfrac{61}{394}< \dfrac{4}{3}\Rightarrow\dfrac{2135}{13790}< \dfrac{4}{3}\)

d) Ta có:

\(\dfrac{2022}{2021}=\dfrac{1}{2021}+1\)

\(\dfrac{10}{9}=\dfrac{1}{9}+1\)

Ta thấy: \(\dfrac{1}{2021}< \dfrac{1}{9}\Rightarrow\dfrac{1}{2021}+1< \dfrac{1}{9}+1\)

Hay \(\dfrac{2022}{2021}< \dfrac{10}{9}\)

e) Ta có:

\(\dfrac{35}{36}=1-\dfrac{1}{36}\)

\(\dfrac{16}{17}=1-\dfrac{1}{17}\)

Ta có: \(\dfrac{1}{36}< \dfrac{1}{17}\Rightarrow1-\dfrac{1}{36}>1-\dfrac{1}{17}\)

Hay \(\dfrac{35}{36}>\dfrac{16}{17}\)

f) Ta có: \(1,3>1,2\)

\(\Rightarrow-1,3< -1,2\)