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a) Ta có : \(\dfrac{-1}{5}< 0< \dfrac{1}{1000}\)
\(\Rightarrow\dfrac{-1}{5}< \dfrac{1}{1000}\)
b) Ta có : \(\dfrac{267}{268}< 1< \dfrac{1347}{1343}\)
=> \(\dfrac{267}{-268}< -\dfrac{1347}{1343}\)
c) \(\dfrac{13}{38}>\dfrac{13}{39}=\dfrac{1}{3}=\dfrac{19}{87}>\dfrac{29}{88}\)
=> \(-\dfrac{13}{38}< \dfrac{29}{-88}\)
d) \(\dfrac{181818}{313131}=\dfrac{18}{31}\)
=> \(-\dfrac{18}{31}=-\dfrac{181818}{313131}\)
So sánh các số hữu tỉ:
a) và
b) và
c) x = -0,75 và
Lời giải:
a)
Vì -22 < -21 và 77> 0 nên x <y
b)
Vì -216 < -213 và 300 > 0 nên y < x
c)
Vậy x=y
Lời giải:
a)
Vì -22 < -21 và 77> 0 nên x <y
b)
Vì -216 < -213 và 300 > 0 nên y < x
c)
Vậy x=y
Áp dụng 1.5 ta có:
a) \(\dfrac{4}{9}< 1\Rightarrow\dfrac{4}{9}< \dfrac{4+9}{9+9}=\dfrac{13}{18}\).
b) \(\dfrac{-15}{7}< 1\Rightarrow\dfrac{-15}{7}< \dfrac{-15+3}{7+3}=\dfrac{-12}{10}=\dfrac{-6}{5}\).
c) \(\dfrac{278}{37}>1\Rightarrow\dfrac{278}{37}>\dfrac{278+9}{37+9}=\dfrac{278}{46}\).
d) \(\dfrac{-157}{623}< 1\Rightarrow\dfrac{-157}{623}< \dfrac{-157+16}{623+16}=\dfrac{-141}{639}=\dfrac{-47}{213}\);
a) \(\dfrac{4}{9}\)và \(\dfrac{13}{18}\)
Ta có : \(\dfrac{4}{9}\)=\(\dfrac{4.2}{9.2}\)=\(\dfrac{8}{18}\)
\(\Rightarrow\)\(\dfrac{8}{18}\)>\(\dfrac{13}{18}\)
giữ nguyên \(\dfrac{13}{18}\) (vì \(8>13\))
- Vậy \(\dfrac{4}{9}>\dfrac{13}{18}\)
b)\(-\dfrac{15}{7}\)và \(-\dfrac{6}{5}\)
Ta có :\(-\dfrac{15}{7}=\dfrac{-15.5}{7.5}=\dfrac{-75}{35}\)
\(\Rightarrow\)\(-\dfrac{75}{35}< \dfrac{-42}{35}\)
\(-\dfrac{6}{5}=\dfrac{-6.7}{5.7}=\dfrac{-42}{35}\) (vì - 75>-42)
- vậy \(\dfrac{-15}{7}< \dfrac{-6}{5}\)
c)\(\dfrac{278}{37}\)và \(\dfrac{287}{46}\)
Ta có :\(\dfrac{278}{37}=\dfrac{278.46}{37.46}=\dfrac{12788}{1702}\)
\(\Rightarrow\)\(\dfrac{12788}{1702}>\dfrac{10286}{1702}\)
\(\dfrac{287}{46}=\dfrac{287.37}{46.37}=\dfrac{10286}{1702}\) (vì 12788>10286)
- vậy \(\dfrac{278}{37}>\dfrac{10286}{46}\)
d)\(-\dfrac{157}{623}\)và \(-\dfrac{47}{213}\)
\(-\dfrac{157}{623}=\dfrac{-157.213}{623.213}=\dfrac{-33441}{132699}\)
\(\Rightarrow\dfrac{-33441}{132699}< \dfrac{-29281}{132699}\)
\(\dfrac{-47}{213}=\dfrac{-47.623}{213.623}=\dfrac{-29281}{132699}\) (vì -33441<-29281)
-vậy \(-\dfrac{157}{623}< -\dfrac{47}{213}\)
a) Ta có:
\(-\dfrac{24}{35}< -\dfrac{24}{30}< -\dfrac{19}{30}\)
\(\Rightarrow x< y\)
b) Ta có:
\(A=\dfrac{2006}{2007}-\dfrac{2007}{2008}+\dfrac{2008}{2009}-\dfrac{2009}{2010}\)
\(A=\left(1-\dfrac{1}{2007}\right)-\left(1-\dfrac{1}{2008}\right)+\left(1-\dfrac{1}{2009}\right)-\left(1-\dfrac{1}{2010}\right)\)
\(A=1-\dfrac{1}{2007}-1+\dfrac{1}{2008}+1-\dfrac{1}{2009}-1+\dfrac{1}{2010}\)
\(A=-\dfrac{1}{2007}+\dfrac{1}{2008}-\dfrac{1}{2009}+\dfrac{1}{2010}\)
Ta lại có:
\(B=-\dfrac{1}{2006.2007}-\dfrac{1}{2008.2009}\)
\(B=-\dfrac{1}{2006}+\dfrac{1}{2007}-\dfrac{1}{2008}+\dfrac{1}{2009}\)
=> Dễ dàng thấy A > B
a) \(\frac{1}{8}>0>\frac{-3}{8}=>\frac{1}{8}>\frac{-3}{8}\)
b) \(\frac{-3}{7}< 0< 2\frac{1}{2}=>\frac{-3}{7}< 2\frac{1}{2}\)
c) \(-3.9< 0< 0.1=>-3.9< 0.1\)
d) \(-2.3< 0< 3.2=>-2.3< 3.2\)
a) Ta có: \(\dfrac{325}{260}< 2< \dfrac{876}{320}\) => \(\dfrac{325}{260}< \dfrac{876}{320}\)
b) Ta có: \(\dfrac{13}{9}< \dfrac{24}{9}=\dfrac{8}{3}\) => \(\dfrac{13}{9}< \dfrac{8}{3}\)
c) Ta có: \(\dfrac{18}{-39}=\dfrac{-18}{39}< \dfrac{-17}{39}< \dfrac{-17}{41}\) => \(\dfrac{18}{-39}< \dfrac{-17}{41}\)
d) Ta có: \(\dfrac{-151515}{232323}=\dfrac{-151515\div10101}{232323\div10101}=\dfrac{-15}{23}\)
Mà \(\dfrac{-15}{25}>\dfrac{-15}{23}\) => \(\dfrac{-15}{25}>\dfrac{-151515}{232323}\)
a) \(\dfrac{325}{260}=\dfrac{5}{4}=\dfrac{100}{80}< \dfrac{219}{80}=\dfrac{876}{320}\)
b) \(\dfrac{13}{9}< \dfrac{24}{9}=\dfrac{8}{3}\)
c) \(\dfrac{18}{-39}=\dfrac{-738}{1599}< \dfrac{-663}{1599}=\dfrac{-17}{41}\)
d) \(\dfrac{-15}{25}=\dfrac{-151515}{252525}< \dfrac{-151515}{232323}\)
a. Ta có:\(\dfrac{-5}{7}\)=\(\dfrac{-5\cdot8}{7\cdot8}\)=\(\dfrac{-40}{56}\)
\(\dfrac{-3}{8}\)=\(\dfrac{-3\cdot7}{8\cdot7}=\dfrac{-21}{56}\)
Ta thấy :\(\dfrac{-40}{56}< \dfrac{-21}{56}\)⇔\(\dfrac{-5}{7}< \dfrac{-3}{8}\)
a)Ta có :
\(-\dfrac{265}{317}< -\dfrac{83}{317}< -\dfrac{83}{111}\Rightarrow-\dfrac{265}{317}< -\dfrac{83}{111}\)
b)Ta có :
\(\dfrac{2002}{2003}< 1< \dfrac{14}{13}\Rightarrow\dfrac{2002}{2003}< \dfrac{14}{13}\)
c)Ta có :
\(\dfrac{-1}{-3}=\dfrac{1}{3}\Rightarrow-\dfrac{27}{463}< 0< \dfrac{1}{3}\Rightarrow-\dfrac{27}{463}< \dfrac{1}{3}\)
\(\dfrac{998}{555}-1=\dfrac{443}{555}\)
\(\dfrac{999}{556}-1=\dfrac{443}{556}\)
\(\dfrac{443}{555}>\dfrac{443}{556}\Rightarrow\dfrac{998}{555}>\dfrac{996}{556}\)
a) <
b) >