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Đầu tiên ta thấy : \(\dfrac{11}{6}>0\) vì đó là số hữu tỉ dương.
\(\dfrac{8}{-9}=\dfrac{-8}{9}< 0\) vì đó là số hữu tỉ âm.
Do đó : \(\dfrac{11}{6}>\dfrac{8}{-9}\)
\(\dfrac{11}{6}>0\)
\(\dfrac{8}{-9}< 0\)
\(\Rightarrow\dfrac{11}{6}>\dfrac{8}{-9}\)
a) \(\dfrac{11}{2}=\dfrac{10+1}{2}=5+\dfrac{1}{2}\)
\(\dfrac{32}{9}=\dfrac{27+5}{9}=3+\dfrac{5}{9}< 5+\dfrac{1}{2}\)
Vậy \(\dfrac{11}{2}>\dfrac{32}{9}\)
b)\(\dfrac{100}{23}=\dfrac{92+8}{23}=4+\dfrac{8}{23}\)
\(\dfrac{302}{123}=\dfrac{246+56}{123}=2+\dfrac{56}{123}< 4+\dfrac{8}{23}\)
Vậy \(\dfrac{100}{23}>\dfrac{302}{123}\)
c) \(\dfrac{515}{605}< \dfrac{515+1}{605+1}=\dfrac{516}{606}\Rightarrow\dfrac{515}{605}< \dfrac{516}{606}\)
\(a)32^9=(2\cdot5)^9=2^{45}=(2^3)^{15}=8^{15}=8^{13}\cdot8^2=8^{13}\cdot2^6\)
\(18^{13}=(9\cdot2)^{13}=9^{13}\cdot2^{13}\)
Vì 913 > 813
213 > 26
=> \(32^9< 18^{13}\)
=> \((-32)^9>(-18)^{13}\)
Còn bài b tự xử
Học tốt
a, -1/4<0
1/100>0
=> -1/4<1/100
b) -11/32=-11.25/ 32.25=-275/800
-25/ 76=-25.11/ 76.11=-275/ 836
=>275/800>275/836
=> -275/800< -275/836
c) -127/128> -1
-1345/1344< -1
=> 127/ -128> -1345/ 1344
d) -171717/ 232323= -17.10101/ 23.10101=-17/23
e) -1/25<0
1/1225>0
=> -1/25< 1/1225
f) 215/216<1
104/103>1
=> 215/216< 104/103
g) -12/19= 19-31/ 19= 1-31/19
-14/17= 17-31/ 17= 1-31/17
mà 31/19< 31/17
=> 1-31/19> 1-31/17
=>-12/19> -14/17
a) Vì \(-45< -16\) nên \(\left(-\dfrac{45}{17}\right)^{15}< \left(\dfrac{-16}{17}\right)^{15}\)
b) Vì \(21< 23\) nên \(\left(-\dfrac{8}{9}\right)^{21}< \left(-\dfrac{8}{9}\right)^{23}\)
c) \(27^{40}=3^{3^{40}}=3^{120}\)
\(64^{60}=8^{2^{60}}=8^{120}\)
Vì \(3< 8\) nên \(3^{120}< 8^{120}\) hay \(27^{40}< 64^{60}\)
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) \(0,3=\dfrac{3}{10}=\dfrac{9}{30}< \dfrac{9+8}{30+8}=\dfrac{17}{38}< \dfrac{19}{38}\Rightarrow0,3< \dfrac{19}{38}\Rightarrow-0,3>\dfrac{-19}{38}\)