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Quy đồng ( đây ngu toán không logic )
a)\(\dfrac{3}{6};\dfrac{2}{6};\dfrac{4}{6}\Rightarrow\dfrac{4}{6}>\dfrac{3}{6}>\dfrac{2}{6}\)
b)\(\dfrac{16}{9};\dfrac{24}{13}=\dfrac{208}{117};\dfrac{216}{117}\Rightarrow\dfrac{216}{117}>\dfrac{208}{117}\)
c)(Trời ơi cái đề bài)
h)\(\dfrac{27}{82};\dfrac{26}{75}=\dfrac{2025}{6150};\dfrac{2132}{6150}\Rightarrow\dfrac{2025}{6150}< \dfrac{2132}{6150}\)
d)(Trời ơi giống câu c)
i)\(\dfrac{-49}{78};\dfrac{64}{-95}=\dfrac{-4655}{7410};\dfrac{4992}{7410}\Rightarrow\dfrac{-4655}{7410}< \dfrac{4992}{7410}\)
P/s : Tự kết luận mỗi câu
a,\(\dfrac{1}{2}=\dfrac{1.3}{2.3}=\dfrac{3}{6}\),\(\dfrac{1}{3}=\dfrac{1.2}{3.2}=\dfrac{2}{6}\),\(\dfrac{2}{3}=\dfrac{2.2}{3.2}=\dfrac{4}{6}\)
vì có mẫu chung là 6 nên ta so sánh tử\(\Rightarrow\)ta so sánh 3,2,4
vì 2<3<4\(\Rightarrow\)\(\dfrac{2}{6}< \dfrac{3}{6}< \dfrac{4}{6}\Rightarrow\dfrac{1}{3}< \dfrac{1}{2}< \dfrac{2}{3}\)
`M=(10^25+1)/(10^26+1)`
`=>10M=(10^26+10)/(10^26+1)=1+9/(10^26+1)``
`CMTT:10N=1+9/(10^27+1)`
Vì `1/(10^26+1)>1/(10^27+1)`
`=>9/(10^26+1)>9/(10^27+1)`
`=>1+9/(10^26+1)>1+9/(10^27+1)`
`=>10M>10N=>M>N`
a) 27/82 < 26/75 ( 2025/6250 < 2132\6250)
b) -49/78 > 64/ -95 ( - 3136/7410 > -4992/7410)
c) ta có: \(A=\frac{54.107-53}{53.107}=\frac{53.107+(107-53)}{53.107+54}=\frac{53.107+54}{53.107+54}=1\)
\(B=\frac{135.269-133}{134.269+135}=\frac{134.269+\left(269-133\right)}{134.269+135}=\frac{134.269+136}{134.269+135}>1\)
\(\Rightarrow A< B\)
d) ta có: \(A=\frac{3^{10}+1}{3^9+1}=\frac{3.\left(3^9+1\right)-2}{3^9+1}=\frac{3.\left(3^9+1\right)}{3^9+1}-\frac{2}{3^9+1}=3-\frac{2}{3^9+1}\)
\(B=\frac{3^9+1}{3^8+1}=\frac{3.\left(3^8+1\right)-2}{3^8+1}=\frac{3.\left(3^8+1\right)}{3^8+1}-\frac{2}{3^8+1}=3-\frac{2}{3^8+1}\)
mà \(\frac{2}{3^9+1}< \frac{2}{3^8+1}\Rightarrow3-\frac{2}{3^9+1}< 3-\frac{2}{3^8+1}\)
=> A < B
c) \(\dfrac{27}{26}\)và\(\dfrac{38}{37}\)
Ta có: \(\dfrac{27}{26}=1+\dfrac{1}{26}\); \(\dfrac{38}{37}=1+\dfrac{1}{37}\)
Vì \(\dfrac{1}{26}>\dfrac{1}{37}\) nên \(\dfrac{27}{26}>\dfrac{38}{37}\)
c: \(\dfrac{27}{26}-1=\dfrac{1}{26}\)
\(\dfrac{38}{37}-1=\dfrac{1}{37}\)
mà \(\dfrac{1}{26}>\dfrac{1}{37}\)
nên \(\dfrac{27}{26}>\dfrac{38}{37}\)
a) 27/82<27/81=3
26/76>26/78=3
suy ra 27/82<26/76
b) -49/78<-49/-95
Mà -49/-95<64/-95
Suy ra -49/78<64/-95
Chúc bạn học tốt nha!