a) \(\dfrac{23}{24}< 1\)

\(\dfrac{24}{23}>1\)

\(\Rightarrow\dfrac{23}{24}< \dfrac{24}{23}\)

b) \(\dfrac{4}{21}< \dfrac{4}{20}=\dfrac{1}{5}=\dfrac{6}{30}< \dfrac{6}{29}\)

c) \(\dfrac{6}{7}=1-\dfrac{1}{7}< \dfrac{8}{9}=1-\dfrac{1}{9}\)

d) \(\dfrac{1212}{1313}=\dfrac{12\times101}{13\times101}=\dfrac{12}{13}\)

a: \(\dfrac{-7}{6}=\dfrac{-7\cdot3}{6\cdot3}=\dfrac{-21}{18}\)

\(\dfrac{-11}{9}=\dfrac{-11\cdot2}{9\cdot2}=\dfrac{-22}{18}\)

mà -21>-22

nên \(-\dfrac{7}{6}>-\dfrac{11}{9}\)

b: \(\dfrac{5}{-7}=\dfrac{-5}{7}=\dfrac{-5\cdot5}{7\cdot5}=\dfrac{-25}{35}\)

\(\dfrac{-4}{5}=\dfrac{-4\cdot7}{5\cdot7}=\dfrac{-28}{35}\)

mà -25>-28

nên \(\dfrac{5}{-7}>\dfrac{-4}{5}\)

c: \(\dfrac{-8}{7}< -1\)

\(-1< -\dfrac{2}{5}\)

Do đó: \(-\dfrac{8}{7}< -\dfrac{2}{5}\)

d: \(-\dfrac{2}{5}< 0\)

\(0< \dfrac{1}{3}\)

Do đó: \(-\dfrac{2}{5}< \dfrac{1}{3}\)

a)\(\dfrac{-8}{9}< \dfrac{-7}{9}\\ \dfrac{6}{7}< \dfrac{11}{10}\)

a) Vì -8<-7 nên \(\dfrac{-8}{9}< \dfrac{-7}{9}\)

b) Ta có: \(\dfrac{6}{7}< 1;\dfrac{11}{10}>1\)

nên \(\dfrac{6}{7}< \dfrac{11}{10}\)

Giải:

a) -8/9 < -7/9

b) Ta có: 6/7 = 60/70

                 11/10 = 77/70

Vì 60/70 < 77/70 nên :

    6/7 < 11/10

a)

Ta có: \(BCNN\left( {10,15} \right) = 30\) nên

\(\begin{array}{l}\dfrac{7}{{10}} = \dfrac{{7.3}}{{10.3}} = \dfrac{{21}}{{30}}\\\dfrac{{11}}{{15}} = \dfrac{{11.2}}{{15.2}} = \dfrac{{22}}{{30}}\end{array}\)

Vì \(21 < 22\) nên \(\dfrac{{21}}{{30}} < \dfrac{{22}}{{30}}\) do đó \(\dfrac{7}{{10}} < \dfrac{{11}}{{15}}\).

b)

Ta có: \(BCNN\left( {8,24} \right) = 24\) nên

\(\dfrac{{ - 1}}{8} = \dfrac{{ - 1.3}}{{8.3}} = \dfrac{{ - 3}}{{24}}\)

Vì \( - 3 >  - 5\) nên \(\dfrac{{ - 3}}{{24}} > \dfrac{{ - 5}}{{24}}\) do đó \(\dfrac{{ - 1}}{8} > \dfrac{{ - 5}}{{24}}\).

2/

a/ \(\dfrac{7}{10}=\dfrac{7.15}{10.15}=\dfrac{105}{150}\)

\(\dfrac{11}{15}=\dfrac{11.10}{15.10}=\dfrac{110}{150}\)

-Vì \(\dfrac{105}{150}< \dfrac{110}{150}\)(105<110)nên \(\dfrac{7}{10}< \dfrac{11}{15}\)

b/ \(\dfrac{-1}{8}=\dfrac{-1.3}{8.3}=\dfrac{-3}{24}\)

-Vì \(\dfrac{-3}{24}>\dfrac{-5}{24}\left(-3>-5\right)\)nên\(\dfrac{-1}{8}>\dfrac{-5}{24}\)

c/\(\dfrac{25}{100}=\dfrac{25:25}{100:25}=\dfrac{1}{4}\)

\(\dfrac{10}{40}=\dfrac{10:10}{40:10}=\dfrac{1}{4}\)

-Vì \(\dfrac{1}{4}=\dfrac{1}{4}\)nên\(\dfrac{25}{100}=\dfrac{10}{40}\)

a/ \(\dfrac{7}{10}< \dfrac{11}{15}\)

c/ \(\dfrac{25}{100}=\dfrac{10}{40}\)

a) 

b) 

c) \(\dfrac{25}{100}=\dfrac{10}{40}\)

a) \(\dfrac{5}{9}< \dfrac{7}{9}\)

b) \(\dfrac{7}{6}>\dfrac{6}{6}\)

c) \(\dfrac{3}{14}< \dfrac{5}{14}\)

d) \(\dfrac{5}{8}< \dfrac{9}{8}\)

a)

MSC: 35

\(\dfrac{4}{7}=\dfrac{4\times5}{7\times5}=\dfrac{20}{35}\)

\(\dfrac{28}{35}\) giữ nguyên

b)

MSC: 100

\(\dfrac{13}{20}=\dfrac{13\times5}{20\times5}=\dfrac{65}{100}\)

c)

MSC: 24

\(\dfrac{5}{6}=\dfrac{5\times4}{6\times4}=\dfrac{20}{24}\)

\(\dfrac{9}{8}=\dfrac{9\times3}{8\times3}=\dfrac{27}{24}\)

a, 4/7 và 28/35

ta có :

4/7=20/35

28/35

b13/20 và 32/100

ta có :

13/20=65/100

32/100

c,5/6,9/8 và 11/24

ta có : 

5/6=20/24

9/8=27/24

11/24

a) \(< \)

b) \(>\)

c) \(< \)

d) \(>\)

e) \(< \)

g) \(>\)

h) \(>\)

k) \(>\)

Do \(\dfrac{{ - 11}}{8} < 0\) và \(\dfrac{1}{{24}} > 0\) nên \(\dfrac{{ - 11}}{8} < \dfrac{1}{{24}}\)