Đáp án + Giải thích các bước giải:

Bài $9$:

$1)$

$\dfrac{56}{57} = 1 - \dfrac{1}{57}$

$\dfrac{57}{58} = 1 - \dfrac{1}{58}$

Mà $\dfrac{1}{57} > \dfrac{1}{58}$

$\Rightarrow 1 - \dfrac{1}{57} < 1 - \dfrac{1}{58}$

$\Rightarrow \dfrac{56}{57} < \dfrac{57}{58}$

$2)$

$\dfrac{15}{16} = 1 - \dfrac{1}{16}$

$\dfrac{19}{20} = 1 - \dfrac{1}{20}$

Mà $\dfrac{1}{16} > \dfrac{1}{20}$

$\Rightarrow 1 - \dfrac{1}{16} < 1 - \dfrac{1}{20}$

$\Rightarrow \dfrac{15}{16} < \dfrac{19}{20}$

$3)$

$\dfrac{43}{42} = 1 + \dfrac{1}{42}$

$\dfrac{53}{52} = 1 + \dfrac{1}{52}$

Mà $\dfrac{1}{42} > \dfrac{1}{52}$

$\Rightarrow 1 + \dfrac{1}{42} > 1 + \dfrac{1}{52}$

$\Rightarrow \dfrac{43}{42} > \dfrac{53}{52}$

$4)$

$\dfrac{29}{14} = 2 + \dfrac{1}{14}$

$\dfrac{31}{15} = 2 +\dfrac{1}{15}$

Mà $\dfrac{1}{14} > \dfrac{1}{15}$

$\Rightarrow 2 + \dfrac{1}{14} > 2 + \dfrac{1}{15}$

$\Rightarrow \dfrac{29}{14} > \dfrac{31}{15}$

$5)$

$-\dfrac{9}{19} = -\dfrac{1}{2} + \dfrac{1}{38}$

$-\dfrac{10}{21} = -\dfrac{1}{2} + \dfrac{1}{42}$

Mà $\dfrac{1}{38} > \dfrac{1}{42}$

$\Rightarrow -\dfrac{1}{2} + \dfrac{1}{38} > -\dfrac{1}{2} + \dfrac{1}{42}$

$\Rightarrow -\dfrac{9}{19} > -\dfrac{10}{21}$

$6)$

$\dfrac{-14}{17} = -1 + \dfrac{3}{17}$

$\dfrac{-21}{24} = -1 + \dfrac{3}{24}$

Mà $\dfrac{3}{17} > \dfrac{3}{24}$

$\Rightarrow -1 + \dfrac{3}{17} > -1 + \dfrac{3}{24}$

$\Rightarrow \dfrac{-14}{17} > \dfrac{-21}{24}$

Bài $10$:

$1) \dfrac{1212}{2323} = \dfrac{12 \cdot 101}{23 \cdot 101} = \dfrac{12}{23}$

$2) \dfrac{414141}{676767} = \dfrac{41 \cdot 10101}{67 \cdot 10101} = \dfrac{41}{67}$

$3) \dfrac{-5959}{4242} = \dfrac{-59 \cdot 101}{42 \cdot 101} = \dfrac{-59}{42}$

$4) \dfrac{1010}{2121} = \dfrac{10 \cdot 101}{21 \cdot 101} = \dfrac{10}{21}$

$\dfrac{101010}{212121} = \dfrac{10 \cdot 10101}{21 \cdot 10101} = \dfrac{10}{21}$

$\Rightarrow \dfrac{1010}{2121} = \dfrac{101010}{212121}$

$5)$

$-\dfrac{333}{666} = -\dfrac{1 \cdot 333}{2 \cdot 333} = -\dfrac{1}{2}$

$\dfrac{444}{-888} = \dfrac{1 \cdot 444}{-2 \cdot 444} = \dfrac{1}{-2}$

$\Rightarrow -\dfrac{333}{666} = \dfrac{444}{-888}$

$6)$

$-\dfrac{555}{888} = -\dfrac{5 \cdot 111}{8 \cdot 111} = -\dfrac{5}{8}$

$\dfrac{-33}{44} = \dfrac{-3 \cdot 11}{4 \cdot 11} = \dfrac{-3}{4}$

Mà $\dfrac{-3}{4} = \dfrac{-6}{8} < \dfrac{-5}{8}$

$\Rightarrow -\dfrac{555}{888} > \dfrac{-33}{44}$