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\(\frac{12}{13}>\frac{22}{33}\)
\(\frac{123}{123}=\frac{124124}{125125}\)
Chuyển từ phân số thành hỗn số :
\(\frac{14}{5}=2\frac{4}{5},\frac{29}{7}=4\frac{1}{7},\frac{100}{24}=4\frac{1}{6},\frac{32}{7}=4\frac{4}{7},\frac{315}{100}=3\frac{3}{20}\)
\(\frac{31}{15}=2\frac{1}{15},\frac{89}{10}=8\frac{9}{10},\frac{25}{6}=4\frac{1}{6},\frac{124}{50}=2\frac{12}{25},\frac{35}{4}=8\frac{3}{4}\)
\(\dfrac{212121}{232323}=\dfrac{212121:10101}{232323:10101}=\dfrac{21}{23}\)
\(\dfrac{123123}{124124}=\dfrac{123123:1001}{124124:1001}=\dfrac{123}{124}\)
Ta có: \(1-\dfrac{21}{23}=\dfrac{2}{23}\) ; \(1-\dfrac{123}{124}=\dfrac{1}{124}=\dfrac{2}{248}\)
\(=>\dfrac{2}{23}>\dfrac{2}{248}\)
\(=>1-\dfrac{21}{23}>1-\dfrac{123}{124}\)
\(=>\dfrac{21}{23}< \dfrac{123}{124}\)
\(=>\dfrac{212121}{232323}< \dfrac{123123}{124124}\)
Ta có :
\(121.124=\left(123-2\right)\left(123+2\right)=123^2-2^2< 123^2\)
\(\Rightarrow A< B\)
a) B = 124 x 122 = (123+1) x (123-1) = 123 x 123 -123 + 123 -1 = A -1
=> B < A
b) B = 986 x 985 = (987-1) x (984+1) = 987 x 984 + 987 - 984 -1 = A +2
=> B > A
\(\frac{85}{168}\) > \(\frac{61}{124}\)
Bài giải
a, Ta có : \(121\cdot124=121\cdot123+121\)
\(123\cdot123=121\cdot123+2\cdot123=121\cdot123+246\)
Vì \(121\cdot123+246>121\cdot123+121\) nên \(123\cdot123>121\cdot124\)
b, Ta có :
\(2004\cdot2004=2002\cdot2004+2\cdot2004=2002\cdot2004+4008\)
\(2002\cdot2006=2002\cdot2004+2\cdot2002=2002\cdot2004+4004\)
Vì \(2002\cdot2004+4008>2002\cdot2004+4004\) nên \(2004\cdot2004>2002\cdot2006\)
Làm thử nha .
\(a,\)Ta có :
\(789^{123}=789^{100}.789^{23}\)
\(1000^{10}=10^{3^{10}}=10^{30}\)
Vì \(789^{100}>10^{30}\)( thấy rõ )
=> 789100.78923 > 1030
Hay \(789^{123}>1000^{10}\)
Ta có : \(\frac{124124}{125125}=\frac{124124:1001}{125125:1001}=\frac{124}{125}\)
\(\frac{123}{124}=1-\frac{1}{124}\); \(\frac{124}{125}=1-\frac{1}{125}\)
Vì 1/124 < 1/125 => 123/124 > 123/125 => 123/124 > 124124/125125
ta có: \(\frac{124124}{125125}=\frac{124}{125}\)
Lại có: \(1-\frac{123}{124}=\frac{1}{124};1-\frac{124}{125}=\frac{1}{125}\)
\(\Rightarrow\frac{1}{124}>\frac{1}{125}\Rightarrow1-\frac{123}{124}>1-\frac{124}{125}\)
\(\Rightarrow\frac{123}{124}< \frac{124}{125}\Rightarrow\frac{123}{124}< \frac{124124}{125125}\)