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 \(\dfrac{5}{9}\) < \(\dfrac{7}{10}\)

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 \(\dfrac{5}{9}\) < \(\dfrac{7}{10}\) 

a, 3/4 và 4/5

\(\frac{3}{4}< \frac{4}{5}vì3.5< 4.4\)

b,2000/1000 và 2/5

ta có \(\frac{2000}{1000}=\frac{2}{1}>1\)và 2/5 < 1

Suy ra \(\frac{2000}{1000}>1>\frac{2}{5}\)

Vậy \(\frac{2000}{1000}>\frac{2}{5}\)

c,7/5 và 9/7

ta có \(\frac{7}{5}>\frac{9}{7}\)vì 7.7 > 5.9

a) 3/4 và 4/5

1 - 3/4 = 1/4

1 - 4/5 = 1/5

Vì 1/4 > 1/5 nên 3/4 < 4/5

b) 2000/1000 và 2/5

2000/1000 > 1

2/5 < 1

2000/1000 > 1 > 2/5 nên 2000/1000 > 2/5

c) 7/5 và 9/7

7/5 - 1 = 2/5

9/7 - 1 = 2/7

Vì 2/5 > 2/7 nên 7/5 > 9/7

Chúc bạn học tốt.

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 \(\dfrac{5}{9}\) < \(\dfrac{7}{10}\) 

2/3=4/6

=>2/3<5/6

Cách 1 : Quy đồng tử số :

\(\frac{2}{5}=\frac{4}{10}\) = \(\frac{4}{10}\) => \(\frac{2}{5}=\frac{4}{10}\)

Cách 2 : Nhân "tích chéo"

So sánh \(\frac{2}{5}\) với \(\frac{4}{10}\) nghĩa là so sánh 2 x 10 với 4 x 5.

Vì 2 x 10 = 20 = 4 x 5 nên \(\frac{2}{5}=\frac{4}{10}\)

Cách 3 : Rút gọn.

\(\frac{4}{10}=\frac{4:2}{10:2}=\frac{2}{5}\). Vậy \(\frac{2}{5}=\frac{4}{10}\)

\(\frac{2}{7}=\frac{2.9}{7.9}=\frac{18}{63}\)

\(\frac{4}{9}=\frac{4.7}{9.7}=\frac{28}{63}\)

 \(Vì\frac{18}{63}<\frac{28}{63}nên\frac{2}{7}<\frac{4}{9}\)

Các câu khác tương tự !!

Bài 1:

a: Cách 1: \(\frac37=\frac{3\cdot9}{7\cdot9}=\frac{27}{63};\frac59=\frac{5\cdot7}{9\cdot7}=\frac{35}{63}\)

mà 27<35

nên \(\frac37<\frac59\)

Cách 2: Ta có: \(\frac37=\frac{3\cdot5}{7\cdot5}=\frac{15}{35}\)

\(\frac59=\frac{5\cdot3}{9\cdot3}=\frac{15}{27}\)

mà \(\frac{15}{35}<\frac{15}{27}\left(35>27\right)\)

nên \(\frac37<\frac59\)

b: Cách 1: \(\frac{6}{12}=\frac{6\cdot3}{12\cdot3}=\frac{18}{36};\frac49=\frac{4\cdot4}{9\cdot4}=\frac{16}{36}\)

mà 18>16

nên \(\frac{6}{12}>\frac49\)

Cách 2: \(\frac{6}{12}=\frac{6\cdot2}{12\cdot2}=\frac{12}{24};\frac49=\frac{4\cdot3}{9\cdot3}=\frac{12}{27}\)

mà \(\frac{12}{24}>\frac{12}{27}\left(24<27\right)\)

nên \(\frac{6}{12}>\frac49\)

c: Cách 1: \(\frac{15}{25}=\frac{15\cdot18}{25\cdot18}=\frac{270}{450};\frac{54}{90}=\frac{54\cdot5}{90\cdot5}=\frac{270}{450}\)

Do đó: \(\frac{15}{25}=\frac{54}{90}\)

Cách 2: \(\frac{15}{25}=\frac{15:5}{25:5}=\frac35;\frac{54}{90}=\frac{54:18}{90:18}=\frac35\)

do đó: \(\frac{15}{25}=\frac{54}{90}\)

d: Cách 1: \(\frac{25}{30}=\frac{25\cdot3}{30\cdot3}=\frac{75}{90};\frac{75}{28}=\frac{75\cdot1}{28\cdot1}=\frac{75}{28}\)

mà \(\frac{75}{90}<\frac{75}{28}\left(90>28\right)\)

nên \(\frac{25}{30}<\frac{75}{28}\)

Cách 2: \(\frac{25}{30}=\frac{25\cdot14}{30\cdot14}=\frac{350}{420}\)

\(\frac{75}{28}=\frac{75\cdot15}{28\cdot15}=\frac{1125}{420}\)

mà 350<1125

nên \(\frac{25}{30}<\frac{75}{28}\)

e: cách 1: \(\frac{27}{45}=\frac{27\cdot4}{45\cdot4}=\frac{108}{180};\frac{18}{36}=\frac{18\cdot5}{36\cdot5}=\frac{90}{180}\)

mà 108>90

nên \(\frac{27}{45}>\frac{18}{36}\)

Cách 2: \(\frac{27}{45}=\frac{27\cdot2}{45\cdot2}=\frac{54}{90}\)

\(\frac{18}{36}=\frac{18\cdot3}{36\cdot3}=\frac{54}{108}\)

mà \(\frac{54}{90}>\frac{54}{108}\left(90<108\right)\)

nên \(\frac{27}{45}>\frac{18}{36}\)