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Ta có:
\(\frac{2}{5}=\frac{8}{20};\frac{4}{2}=\frac{40}{20};\frac{6}{2}=\frac{60}{20};\frac{9}{4}=\frac{45}{20};\frac{5}{4}=\frac{25}{20}\)
Vì \(\frac{8}{20}<\frac{25}{20}<\frac{40}{20}<\frac{45}{20}<\frac{60}{20}\) nên \(\frac{2}{5}<\frac{5}{4}<\frac{4}{2}<\frac{9}{4}<\frac{6}{2}\) và ngược lại:
\(\frac{6}{2}>\frac{9}{4}>\frac{4}{2}>\frac{5}{4}>\frac{2}{5}\)
a) \(\frac{6}{2}=3\) ; \(\frac{2}{5}\)không thể rút gọn
a)
\(\dfrac{6}{12}=\dfrac{6:6}{12:6}=\dfrac{1}{2}\)
\(\Rightarrow\dfrac{1}{2}=\dfrac{1\times2}{2\times2}=\dfrac{2}{4}\)
Mà \(\dfrac{2}{4}< \dfrac{3}{4}\)
Vậy \(\dfrac{6}{12}< \dfrac{3}{4}\).
b)
\(\dfrac{8}{10}=\dfrac{8:2}{10:2}=\dfrac{4}{5}\)
Mà \(\dfrac{2}{5}< \dfrac{4}{5}\)
Vậy \(\dfrac{2}{5}< \dfrac{8}{10}\).
c)
\(\dfrac{40}{35}=\dfrac{40:5}{35:5}=\dfrac{8}{7}\)
Mà \(\dfrac{8}{7}>\dfrac{6}{7}\)
Vậy \(\dfrac{40}{35}>\dfrac{6}{7}\).
d)
\(\dfrac{8}{16}=\dfrac{8:8}{16:8}=\dfrac{1}{2}\)
Mà \(\dfrac{1}{2}< \dfrac{5}{2}\)
Vậy \(\dfrac{8}{16}< \dfrac{5}{2}\).
\(\text{a)}\frac{5}{7}>\frac{4}{7}\)
\(\text{b)}\frac{2}{9}< \frac{3}{11}\)
\(\text{c)}\frac{2007}{2009}< \frac{2009}{2011}\)
\(\text{d)}\frac{39}{35}>\frac{49}{45}\)
1/5 = 21/105 ; 2/105 = 2/105 ; 6/35 = 18/105
Vì 2/105 < 18/105 < 21/105
Vậy 2/105 < 6/35 < 1/5
\(\dfrac{1}{5}=\dfrac{21}{105};\dfrac{2}{105}=\dfrac{2}{105};\dfrac{6}{35}=\dfrac{18}{105}\)
\(\Rightarrow\dfrac{2}{105}< \dfrac{18}{105}< \dfrac{21}{105}\)
\(\Leftrightarrow\dfrac{2}{105}< \dfrac{6}{35}< \dfrac{1}{5}\)