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a) \(33^4=\left(3.11\right)^4=3^4.11^4\\ 44^3=\left(4.11\right)^3=4^3.11^3\)
Ta thấy 34>43 và 114>113 nên 334>443
c) \(54^4=\left(3.18\right)^4=3^4.18^4=3^4.\left(2.9\right)^4=3^4.9^4.2^4=27^4.2^4\\ 21^{12}=\left(3.7\right)^{12}=3^{12}.7^{12}=\left(3^3\right)^4.7^{12}=27^4.7^{12}\)
Ta so sánh 24 với 712
\(7^{12}=\left(7^3\right)^4\)
Nhìn vào ta thấy 2<73 => 24<712=> 544<2112
\(a,\frac{2}{3}>\frac{1}{4}\)
\(b,\frac{7}{10}< \frac{7}{8}\)
\(c,\frac{6}{7}>\frac{3}{5}\)
\(d,\frac{14}{21}< \frac{60}{72}\)
\(e,\frac{16}{9}< \frac{24}{13}\)
\(g,\frac{27}{82}< \frac{26}{75}\)
a 2/3 > 1/4
b 7/10 < 7/8
c6/7 > 3/5
d14/21 < 60/72
e16/9 < 24/13
g27/82<26/75
\(A=\frac{34}{7.13}+\frac{51}{13.22}+\frac{85}{22.37}+\frac{68}{37.49}\)
\(=\frac{17.2}{7.13}+\frac{17.3}{13.22}+\frac{17.5}{22.37}+\frac{17.4}{37.49}\)
\(=17\left(\frac{2}{7.13}+\frac{3}{13.22}+\frac{5}{22.37}+\frac{4}{37.49}\right)\)
\(=\frac{17}{3}\left(\frac{6}{7.13}+\frac{9}{13.22}+\frac{15}{22.37}+\frac{12}{37.49}\right)\)
\(=\frac{17}{3}\left(\frac{1}{7}-\frac{1}{13}+\frac{1}{13}-\frac{1}{22}+...+\frac{1}{37}-\frac{1}{49}\right)\)
\(=\frac{17}{3}\left(\frac{1}{7}-\frac{1}{49}\right)\)\(=\frac{17}{3}.\frac{6}{49}=\frac{17.2}{49}=\frac{34}{49}\)
Có : \(\frac{17}{24}=\frac{34}{48}\)
Vì 48 < 49 => \(\frac{34}{48}>\frac{34}{49}\). Hay \(\frac{17}{24}>A\)
1.
a) \(-\frac{15}{17}>-\frac{19}{21}\)
b)\(-\frac{13}{19}>-\frac{19}{23}\)
c)\(-\frac{23}{49}>-\frac{25}{47}\)
d)\(\frac{317}{633}>\frac{371}{743}\)
e)\(-\frac{24}{35}< -\frac{19}{30}\)
f)\(\frac{12}{17}< \frac{13}{18}\)
g) \(-\frac{17}{26}< -\frac{16}{27}\)
h) \(\frac{84}{-83}< -\frac{337}{331}\)
i) \(-\frac{1941}{1931}< -\frac{2011}{2001}\)
j) \(-\frac{1930}{1945}>-\frac{1996}{2001}\)
k) \(\frac{37}{59}< \frac{47}{59}\)
I) \(-\frac{25}{124}>-\frac{27}{100}\)
m) \(-\frac{97}{201}>-\frac{194}{309}\)
n) \(-\frac{189}{398}< -\frac{187}{394}\)
o) \(-\frac{289}{403}>-\frac{298}{401}\)
c)Ta có: x= -0,375=-3/8 mà y= -3/8 nên x=y
d)Ta có:x= -34/4= -8,5 mà y= -8,6 nên x>y
a: \(-\dfrac{3}{4}=\dfrac{-3\cdot3}{4\cdot3}=\dfrac{-9}{12};\dfrac{-2}{3}=\dfrac{-2\cdot4}{3\cdot4}=\dfrac{-8}{12}\)
mà -9<-8
nên \(-\dfrac{3}{4}< -\dfrac{2}{3}\)
b: \(\dfrac{24}{-60}=\dfrac{-2}{5}=\dfrac{-2\cdot4}{5\cdot4}=\dfrac{-8}{20};\dfrac{-33}{44}=\dfrac{-3}{4}=\dfrac{-3\cdot5}{4\cdot5}=\dfrac{-15}{20}\)
mà -8>-15
nên \(\dfrac{24}{-60}>\dfrac{-33}{44}\)
c: \(-\dfrac{75}{85}=\dfrac{-15}{17}=\dfrac{-15\cdot2}{17\cdot2}=\dfrac{-30}{34};\dfrac{34}{-68}=\dfrac{-1}{2}=\dfrac{-1\cdot17}{2\cdot17}=\dfrac{-17}{34}\)
mà -30<-17
nên \(-\dfrac{75}{85}< \dfrac{34}{-68}\)
a) Ta có:
\(\dfrac{3}{4}=1-\dfrac{1}{4}\)
\(\dfrac{2}{3}=1-\dfrac{1}{3}\)
Mà `3 < 4 =>` \(\dfrac{1}{3}>\dfrac{1}{4}\) => \(1-\dfrac{1}{3}< 1-\dfrac{1}{4}\) => \(\dfrac{2}{3}< \dfrac{3}{4}\) => \(-\dfrac{2}{3}>-\dfrac{3}{4}\)
b) Ta có:
\(\dfrac{24}{60}=\dfrac{2}{5}=0,4\)
\(\dfrac{33}{44}=\dfrac{3}{4}=0,75\)
Mà 0,4 < 0,75 => \(\dfrac{24}{60}< \dfrac{33}{44}\) => \(\dfrac{24}{-60}>-\dfrac{33}{44}\)
c) Ta có:
\(\dfrac{34}{68}=\dfrac{1}{2}\)
\(\dfrac{75}{85}=\dfrac{15}{17}>\dfrac{15}{18}=\dfrac{5}{6}>\dfrac{3}{6}=\dfrac{1}{2}\)
=> \(\dfrac{75}{85}>\dfrac{34}{68}\) => \(\dfrac{-75}{85}< \dfrac{34}{-68}\)