2/7;1/3;3/5;7/8;4/3

là 2/7, 1/3, 3/5, 7/8, 4/3

\(\dfrac{1}{2};\dfrac{2}{3};\dfrac{3}{4};\dfrac{4}{5};\dfrac{5}{6};\dfrac{6}{7};\dfrac{7}{8};\dfrac{8}{9};\dfrac{9}{10}\)

Sắp xếp các phân số sau theo thứ tự tăng dần :

\(\dfrac{1}{2}\);\(\dfrac{2}{3}\);\(\dfrac{3}{4}\);\(\dfrac{4}{5}\);\(\dfrac{5}{6}\);\(\dfrac{6}{7}\);\(\dfrac{7}{8}\);\(\dfrac{8}{9}\);\(\dfrac{9}{10}\)

Quy đồng mẫu số các phân số ta được:3/5=504/840;2/7=240/840;1/3=280/840;4/3=1120/840;7/8=735/840.

Vì 240/840<280/840<504/840<735/840<1120/840 nên ta xếp được:2/7;1/3;3/5;7/8;4/3

1/2 < 2/3 < 3/4 <4/5 < 5/6 <6/7 <7/8 <8/9 < 9/10 

Sắp xép theo thứ tự giảm dần là :

      9/10 ; 8/9 ; 7/8 ; 6/7 ; 5/6 ; 4/5; 3/4 ; 2/3 ; 1/2

9/10,8/9,7/8,6/7,5/6,4/5,3/4,2/3,1/2

9/10>8/9>7/8>6/7>5/6>4/5>3/4>2/3>1/2

\(\frac{3}{2};\frac{4}{3};\frac{5}{4};\frac{6}{5};\frac{7}{6};\frac{8}{7};\frac{9}{8}\)

\(1\frac{1}{2};1\frac{1}{3};1\frac{1}{4};1\frac{1}{5};1\frac{1}{6};1\frac{1}{7};1\frac{1}{8}\)\(\frac{3}{2};\frac{4}{3};\frac{5}{4};\frac{6}{5};\frac{7}{6};\frac{8}{7};\frac{9}{8}\)

Vì \(\frac{1}{2}>\frac{1}{3}>\frac{1}{4}>\frac{1}{5}>\frac{1}{6}>\frac{1}{7}>\frac{1}{8}\)

=> \(1\frac{1}{2}>1\frac{1}{3}>1\frac{1}{4}>1\frac{1}{5}>1\frac{1}{6}>1\frac{1}{7}>1\frac{1}{8}\)

Hay    \(\frac{3}{2}>\frac{4}{3}>\frac{5}{4}>\frac{6}{5}>\frac{7}{6}>\frac{8}{7}>\frac{9}{8}\)

9/8,8/7,7/6,6/5,5/4,4/2,3/2

1/7;2/3;3/4;9/8;6/5

Ta có:
\(\dfrac{6}{5}=\dfrac{6\times168}{5\times168}=\dfrac{1008}{840}\)     ;    \(\dfrac{3}{4}=\dfrac{3\times210}{4\times210}=\dfrac{630}{840}\)     ;     \(\dfrac{9}{8}=\dfrac{9\times105}{8\times105}=\dfrac{945}{840}\) 

\(\dfrac{1}{7}=\dfrac{1\times120}{7\times120}=\dfrac{120}{840}\)     ;    \(\dfrac{2}{3}=\dfrac{2\times280}{3\times280}=\dfrac{560}{840}\)

⇒ \(\dfrac{120}{840}< \dfrac{560}{840}< \dfrac{630}{840}< \dfrac{945}{840}< \dfrac{1008}{840}\) ⇒ \(\dfrac{1}{7}< \dfrac{2}{3}< \)\(\dfrac{3}{4}< \dfrac{9}{8}< \dfrac{6}{5}\)
 

a: \(\frac34=\frac{3\times30}{4\times30}=\frac{90}{120};\frac83=\frac{8\times40}{3\times40}=\frac{320}{120}\) ;

\(\frac58=\frac{5\times15}{8\times15}=\frac{75}{120};\frac{12}{5}=\frac{12\times24}{5\times24}=\frac{288}{120}\) ;

\(\frac12=\frac{1\times60}{2\times60}=\frac{60}{120};\frac43=\frac{4\times40}{3\times40}=\frac{160}{120}\)

TA có: 60<75<90<160<288<320

=>\(\frac{60}{120}<\frac{75}{120}<\frac{90}{120}<\frac{160}{120}<\frac{288}{120}<\frac{320}{120}\)

=>\(\frac12<\frac58<\frac34<\frac43<\frac{12}{5}<\frac83\)

=>\(\frac83>\frac{12}{5}>\frac43>\frac34>\frac58>\frac12\)

b: \(\frac78=1-\frac18;\frac23=1-\frac13;\frac56=1-\frac16\)

\(\frac{14}{15}=1-\frac{1}{15};\frac12=1-\frac12;\frac{18}{19}=1-\frac{1}{19}\)

Ta có: 2<3<6<8<15<19

=>\(\frac12>\frac13>\frac16>\frac18>\frac{1}{15}>\frac{1}{19}\)

=>\(-\frac12<-\frac13<-\frac16<-\frac18<-\frac{1}{15}<-\frac{1}{19}\)

=>\(-\frac12+1<-\frac13+1<-\frac16+1<-\frac18+1<-\frac{1}{15}+1<-\frac{1}{19}+1\)

=>\(\frac12<\frac23<\frac56<\frac78<\frac{14}{15}<\frac{18}{19}\)