So sánh 2 phân số sau với 1: 1212/1213,1221/1212
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Trước khi so sánh, ta phải rút gọn phân số \(\frac{1212}{1515}\)và \(\frac{12}{15}\)
Rút gọn P/S, ta có: \(\frac{1212:101}{1515:101}\)=\(\frac{12:3}{15:3}\)=\(\frac{3}{5}\)(1)
\(\frac{12:3}{15:3}=\frac{3}{5}\)(2)
Từ (1) và (2) => \(\frac{12}{15}=\frac{1212}{1515}\)
Ta có: \(\frac{12}{15}=\frac{12\div3}{15\div3}=\frac{4}{5}\)
\(\frac{1212}{1515}=\frac{1212\div303}{1515\div303}=\frac{4}{5}\)
Mà \(\frac{4}{5}=\frac{4}{5}\)
\(\Rightarrow\frac{12}{15}=\frac{1212}{1515}\)
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\(\dfrac{121212}{131313}=\dfrac{121212:10101}{131313:10101}=\dfrac{12}{13}=1-\dfrac{1}{13}\)
\(\dfrac{1313}{1414}=\dfrac{1313:101}{1414:101}=\dfrac{13}{14}=1-\dfrac{1}{14}\)
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
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\(\frac{12}{15}\) giữ nguyên
\(\frac{1212}{1515}=\frac{12.101}{15.101}=\frac{12}{15}\)
\(\Rightarrow\frac{12}{15}=\frac{1212}{1515}\)
TA CÓ:
\(\frac{1212}{1515}=\frac{12.101}{15.101}=\frac{12}{15}\)
DỄ THẤY 2 BIIỂU THỨC BẰNG NHAU
\(\Rightarrow\frac{12}{15}=\frac{1212}{1515}\)
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\(\dfrac{5}{7}\)>\(\dfrac{6}{21}\)
\(\dfrac{18}{24}\)>\(\dfrac{15}{25}\)
\(\dfrac{12}{13}\)=\(\dfrac{1212}{1313}\)
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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...
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dễ mà :
1, 4/6=2/3
18/27=2/3
nen 4/6=18/27
2,12/20=3/5
22/55=2/5
vi 3/5 > 2/5
nen 12/20>22/55
3, 5/6=1-1/6
1111/1212=1-101/1212
vi 1/6>101/1212 nen 5/6<1111/1212
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Ta có: \(A=\frac{432143214321}{999999999999}=\frac{4321\times100010001}{9999\times100010001}=\frac{4321}{9999}< \frac{1}{2}\)
\(B=\frac{1212+1212+1212+1212}{1919+1919+1919+1919}=\frac{1212\times4}{1919\times4}=\frac{1212}{1919}=\frac{12\times101}{19\times101}=\frac{12}{19}>\frac{1}{2}\)
Do:\(A< \frac{1}{2}< B\Rightarrow A< B\)
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Ta có: \(\frac{1212}{1515}=\frac{12}{15}\)
=>\(\frac{12}{15}=\frac{1212}{1515}\)
Trả lời : 1212/1213<1 , 1221/1212>1
1 > 1212 1213 , 1 < 1221 / 1212