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103và 2100
Ta có:1030=(103)10=100010
2100=(210)10=102410
Vì 1000<1024 nên 1030<2100
5300 và 3453
Ta có:5300=(52)150=25150
3453=(33)151=27151=27.27150
Vì 25 < 27.27 nên 5300<3453
nhớ k ch mình nhé
![](https://rs.olm.vn/images/avt/0.png?1311)
ta có A=\(\frac{17^{18}+1}{17^{19}+1}\)<\(\frac{17^{18}+1+16}{17^{19}+1+16}\) (nếu a/b<1 thì a+c/b+c>a/b)
A<\(\frac{17\left(17^{17}+1\right)}{17\left(17^{18}+1\right)}\)
A,<\(\frac{17^{17}+1}{17^{18}+1}\)=B
hay A<B
\(A=\frac{17^{18}+1}{17^{19}+1}\) với \(B=\frac{17^{17}+1}{17^{18}+1}\)
Ta có :B=\(\frac{17^{17}+1}{17^{18}+1}=\frac{17^{18}+17}{17^{19}+17}\)
Ta có:1-B=\(1-\frac{17^{18}+17}{17^{19}+17}=\frac{17^{19}+17-17^{18}-17}{17^{19}+17}=\frac{17^{19}-17^{18}}{17^{19}+17}\)
1-A=1-\(\frac{17^{18}+1}{17^{19}+1}=\frac{17^{19}+1-17^{18}-1}{17^{19}+1}=\frac{17^{19}-17^{18}}{17^{19}+1}\)
Do \(17^{19}+1< 17^{19}+10\Rightarrow1-A>1-B\)
\(\Rightarrow A< B\)
![](https://rs.olm.vn/images/avt/0.png?1311)
quy đồng các phân số sao cho chúng cùng mẫu là so sánh được
Ta có:
a)18/91=18:91=0,197802197
23/114=23:114=0,201754386
Mà:0,197802197<0,201754386 nên 18/91<23/114
b)21/52=21:52=0,403846153
213/523=213:523=0,407265774
Mà:0,403846153<0,407265774 nên 21/52<213/523
c)1313/9191=1313:9191=0,142857142
1111/7373=1111:7373=0,150684931
Mà:0,142857142<0,150684931 nên 1313/9191<1111/7373
^^^^!~~~
![](https://rs.olm.vn/images/avt/0.png?1311)
a) \(\frac{3}{-4}=\frac{-3}{4};\frac{-1}{-4}=\frac{1}{4}\)
Vì - 3 < 1 nên \(\frac{-3}{4}< \frac{1}{4}\)
hay \(\frac{3}{-4}< \frac{-1}{-4}\)
Quy đồng mẫu ta được:
15/17=15.27/17.27=405/459
25/27=25.17/27.27=425/459
⇒405/459<425/459⇒15/17<25/27
![](https://rs.olm.vn/images/avt/0.png?1311)
câu 1)
\(\dfrac{-12}{18}+\left(\dfrac{-21}{35}\right)=\dfrac{-19}{15}\)
câu 2)
\(-\dfrac{3}{21}+\dfrac{6}{42}=0\)
câu 3)
\(-\dfrac{18}{24}+\dfrac{15}{21}=-\dfrac{1}{28}\)
câu 4)
\(\dfrac{1}{6}+\dfrac{2}{5}=\dfrac{17}{30}\)
câu 5)
\(\dfrac{3}{5}+\left(-\dfrac{7}{4}\right)=-\dfrac{23}{20}\)
câu 6)
\(\left(-2\right)+\left(\dfrac{-5}{8}\right)=\dfrac{-21}{8}\)
câu 7)
\(\dfrac{1}{-8}+\left(-\dfrac{5}{9}\right)=-\dfrac{49}{72}\)
câu 8)
\(\dfrac{4}{13}+\dfrac{12}{39}=\dfrac{8}{13}\)
câu 9)
\(\dfrac{1}{21}+\dfrac{1}{28}=\dfrac{1}{12}\)
câu 10)
\(-\dfrac{3}{29}+\dfrac{16}{58}=\dfrac{5}{29}\)
câu 11)
\(\dfrac{8}{40}+\left(-\dfrac{36}{45}\right)=-\dfrac{3}{5}\)
câu 12)
\(-\dfrac{8}{18}+\left(-\dfrac{15}{27}\right)=-1\)
câu 13)
\(\dfrac{13}{30}+\left(-\dfrac{1}{5}\right)=\dfrac{7}{30}\)
câu 14)
\(\dfrac{2}{21}+\dfrac{1}{28}=\dfrac{11}{84}\)
câu 15)
\(5+\left(-\dfrac{3}{4}\right)=\dfrac{17}{4}\)
câu 16)
\(\dfrac{18}{24}+\dfrac{45}{-10}=-\dfrac{15}{4}\)
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a) 3200=(32)100=9100 ; 2300=(23)100=8100
=> 9100>8100 hay 3200>2300
b) 7150=(712)25=504125 ; 3775=(373)25=5065325
=> 504125<5065325 hay 7150<3775
c)rút gọn
2016014/2017015=2014/2015
2016016014/2017017015=2014/2015
=> 2014/2015 = 2014/2015
![](https://rs.olm.vn/images/avt/0.png?1311)
a, Ta có:
13.14 = 182
9.21 = 189
Vì 182 < 189 nên \(\frac{13}{21}<\frac{9}{14}\)
a ) − 1 < 1 ; b ) − 1 6 > − 1 3 ; c ) − 1 24 < − 1 28 ; d ) 103 100 > 1