so sánh : -121212/232323 và 4343/-5454
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\(\dfrac{212121}{232323}=\dfrac{212121:10101}{232323:10101}=\dfrac{21}{23}\)
\(\dfrac{123123}{124124}=\dfrac{123123:1001}{124124:1001}=\dfrac{123}{124}\)
Ta có: \(1-\dfrac{21}{23}=\dfrac{2}{23}\) ; \(1-\dfrac{123}{124}=\dfrac{1}{124}=\dfrac{2}{248}\)
\(=>\dfrac{2}{23}>\dfrac{2}{248}\)
\(=>1-\dfrac{21}{23}>1-\dfrac{123}{124}\)
\(=>\dfrac{21}{23}< \dfrac{123}{124}\)
\(=>\dfrac{212121}{232323}< \dfrac{123123}{124124}\)
232323/434343=23/43=161/301
6/7=258/301
mà 161<258
nên 232323/434343<6/7
Ta có:\(\dfrac{2323}{9999}=\dfrac{23.101}{99.101}=\dfrac{23}{99}\)
\(\dfrac{232323}{999999}=\dfrac{23.10101}{99.10101}=\dfrac{23}{99}\)
\(\Rightarrow\dfrac{2323}{9999}=\dfrac{232323}{999999}\)
\(\dfrac{121212}{131313}=\dfrac{121212:10101}{131313:10101}=\dfrac{12}{13}\)
Rút gọn 171717/232323 = 17/23
Quy đồng mẫu số hai phân số: 19/2 5= 19x23/25x23 = 437/575 và 17/23 = 17x25/23x25 = 425/575
Ta thấy 437>425 => 437/575>425/575 => 19/25 > 171717/232323
\(\dfrac{121212}{232323}=\dfrac{12x10101}{23x10101}=\dfrac{12}{23}=\dfrac{12.54}{23.54}=\dfrac{648}{1242}\)
\(\dfrac{4343}{5454}=\dfrac{43x101}{54x101}=\dfrac{43}{54}=\dfrac{43.23}{23.54}=\dfrac{989}{1242}\)
mà \(\dfrac{989}{1242}>\dfrac{648}{1242}\)
Nên \(\dfrac{121212}{232323}< \dfrac{4343}{5454}\)
\(\Rightarrow-\dfrac{121212}{232323}>-\dfrac{4343}{5454}\)
\(\Rightarrow\dfrac{-121212}{232323}>\dfrac{4343}{-5454}\)
Đính chính, có thể so sánh cách 2 nhanh hơn.
...\(\dfrac{12}{23}< \dfrac{12+31}{23+31}=\dfrac{43}{54}\)
\(\Rightarrow\dfrac{121212}{232323}< \dfrac{4343}{5454}\)
\(...\Rightarrow\dfrac{-121212}{232323}>\dfrac{4343}{-5454}\)