-2/3; 1/-3; 3/5; 4/5; -8/-7

MSC : `24`

`-5/6=-5.4/6.4=-20/24`

`7/8=7.3/8.3=21/24`

`7/24=7/24`

`-3/4=-3.6/4.6=-18/24`

`2/3=2.8/3.8=16/24`

`1=24/24`

Sắp xếp các phân số sau theo thứ tự tăng dần : 

`-20/24;-18/24;7/24;16/24;21/24;24/24`

\(\dfrac{-1}{2}=\dfrac{-9}{18};\dfrac{-5}{9}=\dfrac{-10}{18};\dfrac{-1}{3}=\dfrac{-6}{18}\)

mà -10<-9<-6<0

nên \(-\dfrac{5}{9}< -\dfrac{1}{2}< -\dfrac{1}{3}< 0\)(1)

Ta có: \(\dfrac{5}{12}=\dfrac{15}{36};\dfrac{7}{18}=\dfrac{14}{36};\dfrac{1}{3}=\dfrac{12}{36}\)

mà \(0< \dfrac{12}{36}< \dfrac{14}{36}< \dfrac{15}{36}\)

nên \(0< \dfrac{1}{3}< \dfrac{7}{18}< \dfrac{5}{12}\left(2\right)\)

Từ (1),(2) suy ra \(-\dfrac{5}{9}< -\dfrac{1}{2}< -\dfrac{1}{3}< \dfrac{1}{3}< \dfrac{7}{18}< \dfrac{5}{12}\)

a) \(\dfrac{-5}{6}=\dfrac{-340}{408}\);\(\dfrac{7}{8}=\dfrac{357}{408}\);\(\dfrac{7}{24}=\dfrac{119}{408}\)

\(\dfrac{16}{17}=\dfrac{384}{408}\); \(\dfrac{-3}{4}=\dfrac{-306}{408}\); \(\dfrac{2}{3}=\dfrac{272}{408}\)

Do đó: \(\dfrac{-5}{6}< \dfrac{-3}{4}< \dfrac{7}{24}< \dfrac{2}{3}< \dfrac{7}{8}< \dfrac{16}{17}\)

a: \(\dfrac{-7}{12}=\dfrac{-7\cdot5}{12\cdot5}=\dfrac{-35}{60};\dfrac{-1}{-15}=\dfrac{1}{15}=\dfrac{4}{60};\dfrac{-5}{4}=\dfrac{-5\cdot15}{4\cdot15}=-\dfrac{75}{60}\)

\(\dfrac{3}{-5}=\dfrac{-3}{5}=\dfrac{-3\cdot12}{5\cdot12}=-\dfrac{36}{60}\)

mà -75<-36<-35<4

nên \(-\dfrac{75}{60}< -\dfrac{36}{60}< -\dfrac{35}{60}< \dfrac{4}{60}\)

=>\(\dfrac{-5}{4}< \dfrac{3}{-5}< \dfrac{-7}{12}< \dfrac{-1}{-15}\)

b: \(\dfrac{-8}{25}+\dfrac{22}{23}+\dfrac{-17}{25}\)

\(=\left(-\dfrac{8}{25}-\dfrac{17}{25}\right)+\dfrac{22}{23}\)

\(=-1+\dfrac{22}{23}=-\dfrac{1}{23}\)

\(\dfrac{-1}{12},\dfrac{-3}{4},\dfrac{2}{9},\dfrac{7}{6}\)

\(-\dfrac{1}{12},-\dfrac{3}{4},\dfrac{2}{9},\dfrac{7}{6}\)

Ta có :

`2/3 = ( 2xx20)/(3xx20)= 40/60`

`(-1)/2 = (-1xx30)/(2xx30)= (-30)/60`

`(-7)/5 = (-7xx12)/(5xx12)=-84/60`

`5/4=(5xx15)/(4xx15)=75/60`

Thứ tự tăng dần là : `(-7)/5 ; (-1)/2 ; 0 ;2/3 ; 5/4`

3/4;2/3;1/3;0;-1/4;-2/5

\(\dfrac{3}{4}\)\(\dfrac{2}{3}\)\(\dfrac{1}{3}\)0\(\dfrac{-1}{4}\)\(\dfrac{-2}{5}\)

trả lời trước mà bị cướp công 

`@` `\text {Ans}`

`\downarrow`

`1,`

Ta có: `12 > 9 > 8 > 7`

`=> 12/8 > 9/8 > 8/8 > 7/8`

`=>` Phân số lớn nhất là `12/8`

`=> A.`

`2,`

So sánh \(\dfrac{3}{4}\text{ ; }\dfrac{9}{32}\)

\(\dfrac{3}{4}=\dfrac{3\times8}{4\times8}=\dfrac{24}{32}\)

Vì `24 > 9 `\(\Rightarrow\dfrac{24}{32}>\dfrac{9}{32}\) \(\Rightarrow\dfrac{3}{4}>\dfrac{9}{32}\)

\(\dfrac{9}{32}\text{;}\dfrac{3}{11}\)

\(\dfrac{9}{32}=\dfrac{9\times11}{32\times11}=\dfrac{99}{352}\)

\(\dfrac{3}{11}=\dfrac{3\times32}{11\times32}=\dfrac{96}{352}\)

Vì `99 > 96 \Rightarrow`\(\dfrac{99}{352}>\dfrac{96}{352}\Rightarrow\dfrac{9}{32}>\dfrac{3}{11}\)

Mà \(\dfrac{3}{11}< \dfrac{3}{4}\); \(\dfrac{9}{32}< \dfrac{3}{4}\)

`\Rightarrow`\(\dfrac{3}{4}>\dfrac{9}{32}>\dfrac{3}{11}\) 

So sánh \(\dfrac{5}{7};\dfrac{3}{4}\)

\(\dfrac{5}{7}=\dfrac{5\times4}{7\times4}=\dfrac{20}{28}\)

\(\dfrac{3}{4}=\dfrac{3\times7}{4\times7}=\dfrac{21}{28}\)

Vì \(20< 21\Rightarrow\dfrac{20}{28}< \dfrac{21}{28}\Rightarrow\dfrac{5}{7}< \dfrac{3}{4}\)

So sánh \(\dfrac{5}{7};\dfrac{9}{32}\)

\(\dfrac{5}{7}=\dfrac{5\times32}{7\times32}=\dfrac{160}{224}\)

\(\dfrac{9}{32}=\dfrac{9\times7}{32\times7}=\dfrac{64}{224}\)

Vì \(160>64\Rightarrow\dfrac{160}{224}>\dfrac{64}{224}\Rightarrow\dfrac{5}{7}>\dfrac{9}{32}\)

`\Rightarrow` Thứ tự sắp xếp các phân số tăng dần là: \(\dfrac{3}{11};\dfrac{9}{32};\dfrac{5}{7};\dfrac{3}{4}\)

Bài 1 : A 12/8

Bài 2 : Theo thứ tự tăng dần là : 3/11, 9/32, 5/7, 3/4