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So sánh \(\frac{-19}{49}\)và\(\frac{-23}{27}\)
Quy đồng lên ta được: \(\frac{-19}{49}=\frac{\left(-19\right).47}{49}=\frac{-893}{2303}\)và\(\frac{-23}{47}=\frac{\left(-23\right).49}{47.49}=\frac{-1127}{2303}\)
Mà: \(\frac{-893}{2303}>\frac{-1127}{2303}\)\(\Rightarrow\frac{-19}{49}>\frac{-23}{47}\)
\(\dfrac{-24}{35}< \dfrac{-19}{30}< \dfrac{-5}{9}< \dfrac{-25}{47}< \dfrac{-23}{49}< 0< \dfrac{124}{2011}\)
a) \(\dfrac{35}{101}=\dfrac{105}{303}< \dfrac{189}{303}\Rightarrow\dfrac{35}{101}< \dfrac{189}{303}\)
b) \(\dfrac{11}{13}< \dfrac{11+2}{13+2}=\dfrac{13}{15}< \dfrac{14}{15}\Rightarrow\dfrac{11}{-13}>\dfrac{-14}{15}\)
c) \(-\dfrac{32}{19}< 0< \dfrac{23}{32}\Rightarrow-\dfrac{32}{19}< \dfrac{23}{32}\)
d) \(1,561< 1,5661\Rightarrow-1,561>-1,5661\)
e) \(0,1=\dfrac{1}{10}=\dfrac{40}{400}< \dfrac{40+56}{400+56}=\dfrac{96}{456}< \dfrac{176}{456}\Rightarrow0,1< \dfrac{176}{456}\)
g) \(0,3=\dfrac{3}{10}=\dfrac{9}{30}< \dfrac{9+8}{30+8}=\dfrac{17}{38}< \dfrac{19}{38}\Rightarrow0,3< \dfrac{19}{38}\Rightarrow-0,3>\dfrac{-19}{38}\)
Lời giải:
a. $\frac{3}{-7}=\frac{-27}{63}$
$\frac{-5}{9}=\frac{-35}{63}$
Do $\frac{27}{63}< \frac{35}{63}$ nên $\frac{-27}{63}> \frac{-35}{63}$
$\Rightarrow \frac{3}{-7}> \frac{-5}{9}$
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b.
$-0,625=\frac{-625}{1000}=\frac{-5}{8}=\frac{-125}{200}$
$\frac{-19}{50}=\frac{-76}{200}> \frac{-125}{200}$
$\Rightarrow -0,625> \frac{-19}{50}$
c.
$-2\frac{5}{9}=-(2+\frac{5}{9})=\frac{-23}{9}=-(\frac{-23}{-9})$
a: \(-\dfrac{19}{49}=\dfrac{-19\cdot47}{49\cdot47}=\dfrac{-893}{2303}\)
\(\dfrac{-23}{47}=\dfrac{-23\cdot49}{47\cdot49}=\dfrac{-1127}{2303}\)
mà -893>-1127
nên \(-\dfrac{19}{49}>-\dfrac{23}{47}\)
b: \(\dfrac{-5}{8}=\dfrac{-5\cdot5}{8\cdot5}=\dfrac{-25}{40}\)
\(\dfrac{7}{-10}=\dfrac{-7}{10}=\dfrac{-7\cdot4}{10\cdot4}=\dfrac{-28}{40}\)
mà -25>-28
nên \(-\dfrac{5}{8}>\dfrac{7}{-10}\)
c: \(\dfrac{24}{35}=\dfrac{24\cdot6}{35\cdot6}=\dfrac{144}{210};\dfrac{19}{30}=\dfrac{19\cdot7}{30\cdot7}=\dfrac{133}{210}\)
mà 144>133
nên \(\dfrac{24}{35}>\dfrac{19}{30}\)