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\(\frac{29}{35}\)<\(\frac{43}{49}\)<\(\frac{31}{35}\)<\(\frac{43}{47}\)
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\(\frac{15}{25}=\frac{3\cdot5}{5\cdot5}=\frac{3}{5}=\frac{21}{35}< \frac{25}{35}=\frac{5\cdot5}{5\cdot7}=\frac{5}{7}\)
\(\frac{17}{49}< \frac{17}{48}< \frac{18}{48}=\frac{3\cdot6}{6\cdot8}=\frac{3}{8}\)
\(\frac{13}{60}< \frac{13}{50}=\frac{26}{100}< \frac{27}{100}\)
\(\frac{43}{47}>\frac{42}{47}>\frac{42}{49}=\frac{6\cdot7}{7\cdot7}=\frac{6}{7}=\frac{30}{35}>\frac{29}{35}\)
\(\frac{1993}{1995}< \frac{1994}{1996}=\frac{997}{998}\)
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a: 14/25=98/175
5/7=125/175
mà 98<125
nên 14/25<5/7
b: 13/60=65/300
27/100=81/300
mà 65<81
nên 13/60<27/100
d: 47/15=329/105
65/21=325/105
mà 329>325
nên 47/15>65/21
e: 3/8=147/392
17/49=136/392
mà 147>136
nên 3/8>17/49
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b) A = 2001 x 2009 và B = 2005 x 2005
\(A=2001\text{*}2009=2001\text{*}\left(2005+4\right)\)
\(=2005\text{*}2001+4\text{*}2001\)
\(B=2005\text{*}2005=\left(2001+4\right)\text{*}2009\)
\(=2001\text{*}2005+4\text{*}2005\)
Vì ta thấy : \(2005\text{*}2001+4\text{*}2001< 2001\text{*}2005+4\text{*}2005\)nên \(2001\text{*}2009< 2005\text{*}2005\)
\(\frac{43}{49}< \frac{31}{35}\)
Ta có:
43/49 = 42/49 + 1/49 = 6/7 + 1/49
31/35 = 30/35 + 1/35 = 6/7 + 1/35
Do 1/49 < 1/35
=> 43/49 < 31/35