Bài 1 So sánh các phân số sau
\(\frac{12}{13}\)và \(\frac{1212}{1313}\)
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\(\dfrac{5}{7}\)>\(\dfrac{6}{21}\)
\(\dfrac{18}{24}\)>\(\dfrac{15}{25}\)
\(\dfrac{12}{13}\)=\(\dfrac{1212}{1313}\)
a) \(\dfrac{12}{14}=\dfrac{1200}{1400}=\dfrac{1400-200}{1400}=1-\dfrac{200}{1400}\)
\(\dfrac{1212}{1414}=\dfrac{1414-200}{1414}=1-\dfrac{200}{1414}\)
vì \(\dfrac{200}{1414}< \dfrac{200}{1400}\)
Nên \(1-\dfrac{200}{1400}< 1-\dfrac{200}{1414}\)
Vậy \(\dfrac{12}{14}< \dfrac{1212}{1414}\)
Các bài sau tương tự
Ta có 1212/1313= 12/13
=> 1212/1313 =12/13
a)Ta có:
\(\frac{1212}{1313}=\frac{12\cdot101}{13\cdot101}=\frac{12}{13}\)
Suy ra \(\frac{12}{13}=\frac{1212}{1313}\)
câu b lạ
\(\dfrac{12}{13}\)= \(\dfrac{12.101}{13.101}\)= \(\dfrac{1212}{1313}\) (1)
\(\dfrac{12}{13}\) = \(\dfrac{12.\left(-10101\right)}{13.\left(-10101\right)}\) = \(\dfrac{-121212}{-131313}\)(2)
Từ (1) và (2) => \(\dfrac{12}{13}=\dfrac{1212}{1313}=\dfrac{-121212}{-131313}\)
\(\dfrac{121212}{131313}=\dfrac{121212:10101}{131313:10101}=\dfrac{12}{13}=1-\dfrac{1}{13}\)
\(\dfrac{1313}{1414}=\dfrac{1313:101}{1414:101}=\dfrac{13}{14}=1-\dfrac{1}{14}\)
Vì \(\dfrac{1}{13}>\dfrac{1}{14}\) nên \(\dfrac{12}{13}< \dfrac{13}{14}\) hay \(\dfrac{1212}{1313}< \dfrac{1313}{1414}\)
b) \(\dfrac{1717}{2525}=\dfrac{1717:101}{2525:101}=\dfrac{17}{25}=\dfrac{51}{75}\)
\(\dfrac{515151}{727272}=\dfrac{515151:10101}{727272:10101}=\dfrac{51}{72}\)
Vì \(\dfrac{51}{75}< \dfrac{51}{72}\) nên \(\dfrac{17}{25}< \dfrac{51}{72}\) hay \(\dfrac{1717}{2525}< \dfrac{515151}{727272}\)
a) \(\dfrac{1212}{1313}=\dfrac{101x12}{101x13}=\dfrac{12}{13}< \dfrac{12+1}{13+1}=\dfrac{13}{14}\)
\(\dfrac{1313}{1414}=\dfrac{101x13}{101x14}=\dfrac{13}{14}\)
Vậy \(\dfrac{1212}{1313}< \dfrac{1313}{1414}\)
Làm tương tự câu b
Ta có: 22/33 = 2/3 = 12/18
12/19 < 12/18
Vậy 12/19 < 22/33
\(\frac{1212}{1313}=\frac{101.12}{101.13}=\frac{12}{13}\)
12/13 = 12/13
Vậy 12/13 = 1212/1313
124124/125125 = \(\frac{1001.124}{1001.125}=\frac{124}{125}\)
1 - 123/124 = 1/124 ; 1 - 124/125 = 1/125
Nên 123/124 < 124/125
Vậy 123/124 < 124124/125125
a) Ta có : 22/33 = 2/3 = 12/18
Vì 12/18 > 12/19 nên 12/19 < 22/33
b) Ta có : 1212/1313 = 12/13
Vì 12/13 = 12/13 nên 12/13 = 1212/1313
c) Ta có : 124124/125125 = 124/125
1 - 123/124 = 1/124
1 - 124/125 = 1/125
Vì 1/124 > 1/125 nên 123/124 < 124124/125125
Ta có: \(\frac{1212}{1313}=\frac{12x101}{13x101}=\frac{12}{13}\)
Vậy \(\frac{12}{13}=\frac{1212}{1313}\)
Ta có: 1212/1313 = 12.101/13.101= 12/13
Vì 12/13 = 12/13 nên 12/13 = 1212/1313
Vây...