\(\dfrac{14}{21};\dfrac{60}{72}\)

\(\dfrac{60}{72}=\dfrac{5}{6}=\dfrac{5\cdot21}{6\cdot21}=\dfrac{105}{126}\)

\(\dfrac{14}{21}=\dfrac{14\cdot6}{21\cdot6}=\dfrac{84}{126}\)

\(\dfrac{84}{123}< \dfrac{105}{126}\Rightarrow\dfrac{14}{21}< \dfrac{60}{72}\)

\(\dfrac{38}{133};\dfrac{129}{344}\)

\(\dfrac{38}{133}=\dfrac{19}{7}=\dfrac{19\cdot8}{7\cdot8}=\dfrac{152}{56}\)

\(\dfrac{129}{344}=\dfrac{3}{8}=\dfrac{3\cdot7}{8\cdot7}=\dfrac{21}{56}\)

\(\dfrac{152}{56}>\dfrac{21}{56}\Rightarrow\dfrac{38}{133}>\dfrac{129}{344}\)

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\(a:ta.c\text{ó}:BCNN:12\\ \dfrac{2}{3}=\dfrac{2\cdot4}{3\cdot4}=\dfrac{8}{12};\dfrac{1}{4}=\dfrac{1\cdot3}{4\cdot3}=\dfrac{3}{12}\\ v\text{ì }\dfrac{8}{12}< \dfrac{3}{12}n\text{ê}n\dfrac{2}{3}< \dfrac{1}{4}\\ b:ta.c\text{ó}:\\ 10=2\cdot5\\ 8=2^3\\ \Rightarrow BCNN=2^3\cdot5=8\cdot5=40\\ \dfrac{7}{10}=\dfrac{7\cdot4}{10\cdot4}=\dfrac{28}{40};\dfrac{7}{8}=\dfrac{7\cdot5}{8\cdot5}=\dfrac{35}{40}\\ v\text{ì }\dfrac{28}{40}< \dfrac{35}{40}n\text{ê}n\dfrac{7}{10}< \dfrac{7}{8}\\ c:ta.c\text{ó}:\\ 7=7;5=5\\ \Rightarrow BCNN=7\cdot5=35\\ \dfrac{6}{7}=\dfrac{6\cdot5}{7\cdot5}=\dfrac{30}{35};\dfrac{3}{5}=\dfrac{3\cdot7}{5\cdot7}=\dfrac{21}{35}\\ v\text{ì }\dfrac{30}{35}>\dfrac{21}{35}n\text{ê}n\dfrac{6}{7}>\dfrac{3}{5}\\ d:ta.c\text{ó}:\\ 21=3\cdot7\\ 72=2^3\cdot3^2\\ \Rightarrow BCNN=2^3\cdot3^2\cdot7=504\\ \dfrac{14}{21}=\dfrac{14\cdot24}{21\cdot24}=\dfrac{336}{504};\dfrac{60}{72}=\dfrac{60\cdot7}{72\cdot7}=\dfrac{420}{504}\\ v\text{ì }\dfrac{336}{504}< \dfrac{420}{504}n\text{ê}n\dfrac{14}{21}< \dfrac{60}{72}\)

đề bài là j???

Đề: So sánh:

e: 38/133=2/7=16/56

129/344=3/8=21/56

mà 16<21

nên 38/133<129/344

f: 11/54=22/108<22/37

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

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: \(1,3>1,2\)

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

a) \(\dfrac{-1}{20}=\dfrac{-7}{140}\)

\(\dfrac{5}{7}=\dfrac{100}{140}\)

mà -7<100

nên \(-\dfrac{1}{20}< \dfrac{5}{7}\)

b) \(\dfrac{216}{217}< 1\)

\(1< \dfrac{1164}{1163}\)

nên \(\dfrac{216}{217}< \dfrac{1164}{1163}\)

c) \(\dfrac{-12}{17}=\dfrac{-180}{255}\)

\(\dfrac{-14}{15}=\dfrac{-238}{255}\)

mà -180>-238

nên \(-\dfrac{12}{17}>\dfrac{-14}{15}\)

d) \(\dfrac{27}{29}>0\)

\(0>-\dfrac{2727}{2929}\)

nên \(\dfrac{27}{29}>-\dfrac{2727}{2929}\)

a)

Có: 

\(2\sqrt{29}=\sqrt{4.29}=\sqrt{116}\\ 3\sqrt{13}=\sqrt{9.13}=\sqrt{117}\)

Vì \(\sqrt{117}>\sqrt{116}\)  nên \(3\sqrt{13}>2\sqrt{29}\)

b)

Có:

\(\dfrac{5}{4}\sqrt{2}=\sqrt{\dfrac{25}{16}.2}=\sqrt{\dfrac{25}{8}}\)

\(\dfrac{3}{2}\sqrt{\dfrac{3}{2}}=\sqrt{\dfrac{9}{4}.\dfrac{3}{2}}=\sqrt{\dfrac{27}{8}}\)

Do \(\sqrt{\dfrac{27}{8}}>\sqrt{\dfrac{25}{8}}\)  nên \(\dfrac{3}{2}\sqrt{\dfrac{3}{2}}>\dfrac{5}{4}\sqrt{2}\)

c)

Có:

\(5\sqrt{2}=\sqrt{25.2}=\sqrt{50}\)

\(4\sqrt{3}=\sqrt{16.3}=\sqrt{48}\)

Vì \(\sqrt{50}>\sqrt{48}\) nên \(5\sqrt{2}>4\sqrt{3}\)

d)

Có:

\(\dfrac{5}{2}\sqrt{\dfrac{1}{6}}=\sqrt{\dfrac{25}{4}.\dfrac{1}{6}}=\sqrt{\dfrac{25}{24}}\)

\(6\sqrt{\dfrac{1}{37}}=\sqrt{36.\dfrac{1}{37}}=\sqrt{\dfrac{36}{37}}\)

lại có: \(\dfrac{25}{24}>\dfrac{36}{37}\)

 \(\Rightarrow\dfrac{5}{2}\sqrt{\dfrac{1}{6}}>6\sqrt{\dfrac{1}{37}}\)

help 

Bài 21: 

Ta có: \(\dfrac{x+1}{99}+\dfrac{x+2}{98}+\dfrac{x+3}{97}+\dfrac{x+4}{96}=-4\)

\(\Leftrightarrow\dfrac{x+1}{99}+1+\dfrac{x+2}{98}+1+\dfrac{x+3}{97}+1+\dfrac{x+4}{96}+1=0\)

\(\Leftrightarrow\dfrac{x+100}{99}+\dfrac{x+100}{98}+\dfrac{x+100}{97}+\dfrac{x+100}{96}=0\)

\(\Leftrightarrow\left(x+100\right)\left(\dfrac{1}{99}+\dfrac{1}{98}+\dfrac{1}{97}+\dfrac{1}{96}\right)=0\)

mà \(\dfrac{1}{99}+\dfrac{1}{98}+\dfrac{1}{97}+\dfrac{1}{96}>0\)

nên x+100=0

hay x=-100

Vậy: x=-100

a: 14/21=2/3=4/6

60/72=5/6

mà 4<5

nên 14/21<60/72

b: 38/133=2/7=16/56

129/344=3/8=21/56

mà 16<21

nên 38/133<129/344