Đáp án:
$\rm M=40$
Giải thích các bước giải:
$\rm M=\dfrac{92-\dfrac{1}{9}-\dfrac{2}{10}-\dfrac{3}{11}\ \ \!\!\!-\ \!.\!.\!.\ \!\!-\dfrac{90}{98}-\dfrac{91}{99}-\dfrac{92}{100}}{\dfrac{1}{45}+\dfrac{1}{50}+\dfrac{1}{55}\ \ \!\!\!+\ \!.\!.\!.\;\!+\ \dfrac{1}{495}+\dfrac{1}{500}}$
$\Rightarrow\rm M=\dfrac{\left(1-\dfrac{1}{9}\right)+\left(1-\dfrac{2}{10}\right)+\ \!.\!.\!.\;\!+\left(1-\dfrac{91}{99}\right)+\left(1-\dfrac{92}{100}\right)}{\dfrac{1}{5}\cdot\left(\dfrac{1}{9}+\dfrac{1}{10}+\dfrac{1}{11}\ \!\;\!\!+\ \!.\!.\!.\;\!+\ \dfrac{1}{99}+\dfrac{1}{100}\right)}$
$\Rightarrow\rm M=\dfrac{\dfrac{8}{9}+\dfrac{8}{10}+\dfrac{8}{11}\ \;\!\!\!+\ \!.\!.\!.\ \!\!+\dfrac{8}{99}+\dfrac{8}{100}}{\dfrac{1}{5}\cdot\left(\dfrac{1}{9}+\dfrac{1}{10}+\dfrac{1}{11}\ \!\;\!\!+\ \!.\!.\!.\;\!+\ \dfrac{1}{99}+\dfrac{1}{100}\right)}$
$\Rightarrow\rm M=\dfrac{8\cdot\left(\dfrac{1}{9}+\dfrac{1}{10}+\dfrac{1}{11}\ \;\!\!\!+\ \!.\!.\!.\ \!\!+\dfrac{1}{99}+\dfrac{1}{100}\right)}{\dfrac{1}{5}\cdot\left(\dfrac{1}{9}+\dfrac{1}{10}+\dfrac{1}{11}\ \!\;\!\!+\ \!.\!.\!.\;\!+\ \dfrac{1}{99}+\dfrac{1}{100}\right)}$
$\Rightarrow\rm M=\dfrac{8}{\dfrac{1}{5}}$
$\Rightarrow\rm M=8\cdot5$
$\Rightarrow\rm M=40$
Vậy $\rm M=40$.
