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\(\frac{2003.2004-1}{2003.2004}=\frac{2003.2004}{2003.2004}-\frac{1}{2003.2004}=1-\frac{1}{2003.2004}\)
\(\frac{2004.2005-1}{2004.2005}=\frac{2004.2005}{2004.2005}-\frac{1}{2004.2005}=1-\frac{1}{2004.2005}\)
Vì \(\frac{1}{2003.2004}>\frac{1}{2004.2005}\)
=> \(1-\frac{1}{2003.2004}< 1-\frac{1}{2004.2005}\)
=> \(\frac{2003.2004-1}{2003.2004}< \frac{2004.2005-1}{2004.2005}\)
\(\frac{2003.2004-1}{2003.2004}=\frac{2003.2004}{2003.2004}-\frac{1}{2003.2004}=1-\frac{1}{2003.2004}\)
\(\frac{2004.2005-1}{2004.2005}=\frac{2004.2005}{2004.2005}-\frac{1}{2004.2005}=1-\frac{1}{2004.2005}\)
Vì \(\frac{1}{2003.2004}>\frac{1}{2004.2005}\)
=> \(1-\frac{1}{2003.2004}< 1-\frac{1}{2004.2005}\)
=> \(\frac{2003.2004-1}{2003.2004}< \frac{2004.2005-1}{2004.2005}\)
a) Ta có: \(\frac{179}{197}< 1\)và \(\frac{971}{917}>1\)
\(\Rightarrow\frac{179}{197}< 1< \frac{971}{917}\)
\(\Rightarrow\frac{179}{197}< \frac{971}{917}\)
b)Ta có: \(\frac{64}{85}< \frac{64}{81}\) mà \(\frac{73}{81}>\frac{64}{81}\)
\(\Rightarrow\frac{64}{85}< \frac{64}{81}< \frac{73}{81}\)
\(\Rightarrow\frac{64}{85}< \frac{73}{81}\)
Tự làm tiếp nha ~
a) Vì 179/197 < 1 ; 971/917 > 1
=> 179/197 < 971/917
b) Vì 64/85 < 64/81 < 73/81
=> 64/85 < 73/81
c) Ta có: 456/461 = 1 - 5/461 ; 123/128 = 1 - 5/128
Vì 5/461 < 5/128 => 1 - 5/461 > 1 - 5/128
=> 456/461 > 123/128
d) 53/57 = 530/570
Áp dụng a/b < 1 => a/b < a+m/b+m (a,b,m thuộc N*)
Do 530/570 < 1 => 530/570 < 530+1/570+1
=> 53/57 < 531/571
e) Ta có: 58/89 > 58/87 = 2/3
36/53 < 36/54 = 2/3
=> 58/89 > 36/53
g) Ta có: 11/32 > 11/33 = 1/3
16/49 < 16/48 = 1/3
=> 11/32 > 16/49
1.\(\frac{456}{461}va\frac{123}{128}\)
Ta có: \(\frac{456}{461}+\frac{5}{461}=1\)
\(\frac{123}{128}+\frac{5}{128}=1\)
vì \(\frac{5}{461}< \frac{5}{128}\)nên \(\frac{456}{461}>\frac{123}{128}\)
2.\(\frac{53}{57}va\frac{531}{571}\)
Vì \(\frac{53}{57}< 1\)
\(\Rightarrow\frac{53}{57}=\frac{530}{570}< \frac{530+1}{570+1}=\frac{531}{571}\)
\(\Rightarrow\frac{53}{57}< \frac{531}{571}\)
a) 456/461 > 123/128
b)11/32 > 16/49
c)3535.232323/353535.2323 < 3535/3434
d)53/57 < 531/571
a) 12 < 13; 49 > 47 => 12/49 < 13/47
b) 64 < 73; 85 > 81 => 64/85 < 73/81
c) 19 > 17; 31 < 35 => 19/31 > 17/35
d) 67/77 = 1 - 10/77; 73/83 = 1- 10/83. Mà 10/77 > 10/83 => 67/77 < 73/83.
e) 456/461 = 1 - 5/461; 123/128 = 1 - 5/128. Mà 5/461 < 5/128 => 456/461 > 123/128.
f) 149/157 = 1 - 8/157; 449/458 = 1 - 9/458. Mà 8/157 = 16/314 > 9/458 => 149/157 < 449/458.
a)
\(\frac{64}{85}< \frac{64}{81}< \frac{73}{81}\)
=>\(\frac{64}{85}< \frac{73}{81}\)
b)
\(\frac{25}{26}=\frac{25.1010}{26.1010}=\frac{25250}{26260}\)
Ta có: \(1-\frac{25250}{26260}=\frac{1010}{26260}\)
\(1-\frac{25251}{26261}=\frac{1010}{26261}\)
Vì \(\frac{1010}{26260}>\frac{1010}{26261}\) nên \(\frac{25}{26}< \frac{25251}{26261}\)
a)\(\frac{64}{85}\)<\(\frac{64}{81}\)<\(\frac{73}{81}\)
b)\(\frac{25}{26}\)=\(\frac{25250}{26260}\)=\(1\)- \(\frac{1010}{26260}\)< \(1\)- \(\frac{1010}{26261}\)= \(\frac{25251}{26261}\)