a) Vì \(\frac{8}{9}< 1\)và \(\frac{7}{5}>1\)nên \(\frac{8}{9}< 1< \frac{7}{5}\)vậy \(\frac{8}{9}< \frac{7}{5}\)

b) Vì \(\frac{3}{4}< 1\)và \(\frac{5}{4}>1\)nên\(\frac{3}{4}< 1< \frac{5}{4}\)vậy \(\frac{3}{4}< \frac{5}{4}\)

Đáp số: a) \(\frac{8}{9}< \frac{7}{5}\)

             b) \(\frac{3}{4}< \frac{5}{4}\)

8/9 và 7/5

-> 7/5 lớn hơn vì mấu nhỏ hơn  3/4 và 5/4 5/4 lớn hơn vì tử lớn hơn

a: 11/10>1>10/11

b: 4/9=44/99

c: 15/25=3/5

12/15=4/5

mà 3/5<4/5

nên 15/25<12/15

a: 11/10>1>10/11

b: 4/9=44/99

c: 15/25=3/5

12/15=4/5

mà 3/5<4/5

nên 15/25<12/15

a; Cách một: 

     \(\dfrac{2}{9}\) = \(\dfrac{2\times2}{9\times2}\) = \(\dfrac{4}{18}\)  < \(\dfrac{4}{10}\) Vậy \(\dfrac{2}{9}\) < \(\dfrac{4}{10}\)

     \(\dfrac{4}{9}\) = \(\dfrac{4\times3}{9\times3}\) = \(\dfrac{12}{27}\); \(\dfrac{6}{10}\) = \(\dfrac{6\times2}{10\times2}\) = \(\dfrac{12}{20}\) 

 Vì \(\dfrac{12}{27}\) < \(\dfrac{12}{20}\) vậy \(\dfrac{4}{9}\) < \(\dfrac{12}{20}\)

     \(\dfrac{3}{8}\) = \(\dfrac{3\times4}{8\times4}\) = \(\dfrac{12}{24}\);   \(\dfrac{4}{7}\) = \(\dfrac{4\times3}{7\times3}\) = \(\dfrac{12}{21}\)

Vậy \(\dfrac{3}{8}\) < \(\dfrac{4}{7}\)

    \(\dfrac{5}{9}\) = \(\dfrac{5\times7}{9\times7}\) = \(\dfrac{35}{63}\); \(\dfrac{7}{10}\) = \(\dfrac{7\times5}{10\times5}\) = \(\dfrac{35}{50}\)

Vì \(\dfrac{35}{63}\) < \(\dfrac{35}{50}\) vậy \(\dfrac{5}{9}\) < \(\dfrac{7}{10}\)

     Cách hai:

a; \(\dfrac{2}{9}\) = \(\dfrac{2\times10}{9\times10}\) = \(\dfrac{20}{90}\); \(\dfrac{4}{10}\)  = \(\dfrac{4\times9}{10\times9}\) = \(\dfrac{36}{90}\) 

Vì \(\dfrac{20}{90}\) < \(\dfrac{36}{90}\) vậy \(\dfrac{2}{9}\) < \(\dfrac{4}{10}\)

b; \(\dfrac{4}{9}\) = \(\dfrac{4\times10}{9\times10}\) = \(\dfrac{40}{90}\); \(\dfrac{6}{10}\) = \(\dfrac{6\times9}{10\times9}\) = \(\dfrac{54}{90}\)

   Vì \(\dfrac{40}{90}\) < \(\dfrac{54}{90}\) vậy \(\dfrac{4}{9}\) < \(\dfrac{6}{10}\)

c; \(\dfrac{3}{8}\) = \(\dfrac{3\times7}{8\times7}\) = \(\dfrac{21}{56}\); \(\dfrac{4}{7}\) =  \(\dfrac{4\times8}{7\times8}\) = \(\dfrac{32}{56}\)

Vì \(\dfrac{21}{56}\) < \(\dfrac{32}{56}\) vậy \(\dfrac{3}{8}\) < \(\dfrac{4}{7}\)

d; \(\dfrac{5}{9}\) = \(\dfrac{5\times10}{9\times10}\) = \(\dfrac{50}{90}\); \(\dfrac{7}{10}\) = \(\dfrac{7\times9}{10\times9}\) = \(\dfrac{63}{90}\)

Vì \(\dfrac{50}{90}\) < \(\dfrac{63}{90}\) vậy \(\dfrac{5}{9}\) < \(\dfrac{7}{10}\) 

   Cách ba:

a; \(\dfrac{2}{9}\) < \(\dfrac{2+2}{9+2}\) = \(\dfrac{4}{11}\) < \(\dfrac{4}{10}\) vậy \(\dfrac{2}{9}\) < \(\dfrac{4}{10}\)

b; \(\dfrac{4}{9}\) < \(\dfrac{4+2}{9+2}\) < \(\dfrac{6}{11}\) < \(\dfrac{6}{10}\) vậy \(\dfrac{4}{9}\) < \(\dfrac{6}{10}\)

c; \(\dfrac{3}{8}\) < \(\dfrac{3+1}{8+1}\) = \(\dfrac{4}{9}\) < \(\dfrac{4}{7}\) vậy \(\dfrac{3}{8}\) < \(\dfrac{4}{7}\)

d; \(\dfrac{5}{9}\) < \(\dfrac{5+2}{9+2}\) = \(\dfrac{7}{11}\) < \(\dfrac{7}{10}\) vậy \(\dfrac{5}{9}\) < \(\dfrac{7}{10}\)

3/8 <4/7

5/9<7/10

           Cách 1: 

\(\dfrac{3}{8}\) = \(\dfrac{3\times4}{8\times4}\) = \(\dfrac{12}{32}\); \(\dfrac{4}{7}\) = \(\dfrac{4\times3}{7\times3}\) = \(\dfrac{12}{21}\)

Vì \(\dfrac{12}{32}\) < \(\dfrac{12}{21}\) nên \(\dfrac{3}{8}\) < \(\dfrac{4}{7}\)

\(\dfrac{5}{9}\) = \(\dfrac{5\times7}{9\times7}\) = \(\dfrac{35}{63}\); \(\dfrac{7}{10}\) = \(\dfrac{7\times5}{5\times10}\) = \(\dfrac{35}{50}\)

Vì \(\dfrac{35}{65}\) < \(\dfrac{35}{50}\) nên \(\dfrac{5}{9}\) < \(\dfrac{7}{10}\)

             Cách hai:

\(\dfrac{3}{8}\) = \(\dfrac{3\times7}{8\times7}\) = \(\dfrac{21}{56}\); \(\dfrac{4}{7}\) = \(\dfrac{4\times8}{7\times8}\) = \(\dfrac{32}{56}\)

Vì \(\dfrac{21}{56}\) < \(\dfrac{32}{56}\) nên \(\dfrac{3}{8}\) < \(\dfrac{4}{7}\)

\(\dfrac{5}{9}\) = \(\dfrac{5\times10}{9\times10}\) = \(\dfrac{50}{90}\); \(\dfrac{7}{10}\) = \(\dfrac{7\times9}{10\times9}\) = \(\dfrac{63}{90}\)

Vì \(\dfrac{50}{90}\) < \(\dfrac{63}{90}\) nên \(\dfrac{5}{9}\) < \(\dfrac{7}{10}\)

a; Cách một: 

     \(\dfrac{2}{9}\) = \(\dfrac{2\times2}{9\times2}\) = \(\dfrac{4}{18}\)  < \(\dfrac{4}{10}\) Vậy \(\dfrac{2}{9}\) < \(\dfrac{4}{10}\)

     \(\dfrac{4}{9}\) = \(\dfrac{4\times3}{9\times3}\) = \(\dfrac{12}{27}\); \(\dfrac{6}{10}\) = \(\dfrac{6\times2}{10\times2}\) = \(\dfrac{12}{20}\) 

 Vì \(\dfrac{12}{27}\) < \(\dfrac{12}{20}\) vậy \(\dfrac{4}{9}\) < \(\dfrac{12}{20}\)

     \(\dfrac{3}{8}\) = \(\dfrac{3\times4}{8\times4}\) = \(\dfrac{12}{24}\);   \(\dfrac{4}{7}\) = \(\dfrac{4\times3}{7\times3}\) = \(\dfrac{12}{21}\)

Vậy \(\dfrac{3}{8}\) < \(\dfrac{4}{7}\)

    \(\dfrac{5}{9}\) = \(\dfrac{5\times7}{9\times7}\) = \(\dfrac{35}{63}\); \(\dfrac{7}{10}\) = \(\dfrac{7\times5}{10\times5}\) = \(\dfrac{35}{50}\)

Vì \(\dfrac{35}{63}\) < \(\dfrac{35}{50}\) vậy \(\dfrac{5}{9}\) < \(\dfrac{7}{10}\)

       Cách hai:

a; \(\dfrac{2}{9}\) = \(\dfrac{2\times10}{9\times10}\) = \(\dfrac{20}{90}\); \(\dfrac{4}{10}\)  = \(\dfrac{4\times9}{10\times9}\) = \(\dfrac{36}{90}\) 

Vì \(\dfrac{20}{90}\) < \(\dfrac{36}{90}\) vậy \(\dfrac{2}{9}\) < \(\dfrac{4}{10}\)

b; \(\dfrac{4}{9}\) = \(\dfrac{4\times10}{9\times10}\) = \(\dfrac{40}{90}\); \(\dfrac{6}{10}\) = \(\dfrac{6\times9}{10\times9}\) = \(\dfrac{54}{90}\)

   Vì \(\dfrac{40}{90}\) < \(\dfrac{54}{90}\) vậy \(\dfrac{4}{9}\) < \(\dfrac{6}{10}\)

c; \(\dfrac{3}{8}\) = \(\dfrac{3\times7}{8\times7}\) = \(\dfrac{21}{56}\); \(\dfrac{4}{7}\) =  \(\dfrac{4\times8}{7\times8}\) = \(\dfrac{32}{56}\)

Vì \(\dfrac{21}{56}\) < \(\dfrac{32}{56}\) vậy \(\dfrac{3}{8}\) < \(\dfrac{4}{7}\)

d; \(\dfrac{5}{9}\) = \(\dfrac{5\times10}{9\times10}\) = \(\dfrac{50}{90}\); \(\dfrac{7}{10}\) = \(\dfrac{7\times9}{10\times9}\) = \(\dfrac{63}{90}\)

Vì \(\dfrac{50}{90}\) < \(\dfrac{63}{90}\) vậy \(\dfrac{5}{9}\) < \(\dfrac{7}{10}\) 

     Cách ba:

a; \(\dfrac{2}{9}\) < \(\dfrac{2+2}{9+2}\) = \(\dfrac{4}{11}\) < \(\dfrac{4}{10}\) vậy \(\dfrac{2}{9}\) < \(\dfrac{4}{10}\)

b; \(\dfrac{4}{9}\) < \(\dfrac{4+2}{9+2}\) < \(\dfrac{6}{11}\) < \(\dfrac{6}{10}\) vậy \(\dfrac{4}{9}\) < \(\dfrac{6}{10}\)

c; \(\dfrac{3}{8}\) < \(\dfrac{3+1}{8+1}\) = \(\dfrac{4}{9}\) < \(\dfrac{4}{7}\) vậy \(\dfrac{3}{8}\) < \(\dfrac{4}{7}\)

d; \(\dfrac{5}{9}\) < \(\dfrac{5+2}{9+2}\) = \(\dfrac{7}{11}\) < \(\dfrac{7}{10}\) vậy \(\dfrac{5}{9}\) < \(\dfrac{7}{10}\)

\(\frac{23}{3}>\frac{15}{2}\)

\(\frac{14}{7}>\frac{2}{9}\)

\(\frac{12}{13}< \frac{13}{14}\)

\(\frac{17}{16}< \frac{16}{15}\)

\(\frac{8}{6}>\frac{42}{43}\)