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Ta có : \(\frac{11}{12}=\frac{11.10}{12.10}=\frac{110}{120}\)
\(\frac{9}{10}=\frac{9.12}{10.12}=\frac{108}{120}\)
Ta thấy \(\frac{110}{120}>\frac{108}{120}\Rightarrow\frac{11}{20}>\frac{9}{10}\)
Vậy \(\frac{11}{20}>\frac{9}{10}\)
a) \(A=\frac{2007}{2009}\&B=\frac{2009}{2011}\Rightarrow\frac{A}{B}=\frac{2007.2011}{2009^2}=\frac{\left(2009-2\right)\left(2009+2\right)}{2009^2}=\frac{2009^2-4}{2009^2}< 1\)
=> A<b
a) Ta có : 1 - \(\frac{2007}{2009}\)= \(\frac{2}{2009}\); 1 - \(\frac{2009}{2011}\)= \(\frac{2}{2011}\)
Vì \(\frac{2}{2009}\)> \(\frac{2}{2011}\)nên \(\frac{2007}{2009}\)< \(\frac{2009}{2011}\)
bạn Đinh Hải Tùng có thể viết các bước giải ra hộ mình được ko ?
a) \(\frac{5}{6}\)= \(\frac{15}{18}\); b) \(\frac{99}{100}\)< \(\frac{100}{99}\); c ) \(\frac{15}{17}\)> \(\frac{13}{18}\)vì \(\frac{15}{17}\)> \(\frac{15}{18}\)> \(\frac{13}{18}\);
d) \(\frac{222}{333}\)= \(\frac{2}{3}\)\(=1-\frac{1}{3}\); \(\frac{3333}{4444}\)= \(\frac{3}{4}\)= \(1-\frac{1}{4}\); vì \(\frac{1}{3}\)> \(\frac{1}{4}\)nên \(\frac{222}{333}\)< \(\frac{3333}{4444}\)
e) \(\frac{292929}{272727}\)= \(\frac{29}{27}\)= \(1+\frac{2}{17}\); \(\frac{347347}{345345}\)= \(\frac{347}{345}\)= \(1+\frac{2}{345}\)nên \(\frac{292929}{272727}\)> \(\frac{347347}{345345}\)
Quy đồng tử số : 6/7 = 6 x20/7 x 20 = 120/140 . Vì 140 lớn hơn 137 nen 120/140 < 120/137 hay 6/7 < 120/137 .Vay 6/7 < 120/37.
ta có: \(1-\frac{17}{20}=\frac{3}{20};1-\frac{22}{25}=\frac{3}{25}\)
\(\Rightarrow\frac{3}{20}>\frac{3}{25}\Rightarrow1-\frac{17}{20}>1-\frac{22}{25}\)
\(\Rightarrow\frac{17}{20}< \frac{22}{25}\)
Cần nhớ:
\(\frac{a}{b}< 1\Rightarrow\frac{a}{b}< \frac{a+n}{b+n}\left(n\inℕ^∗\right)\)
\(\frac{a}{b}>1\Rightarrow\frac{a}{b}>\frac{a+n}{b+n}\left(n\inℕ^∗\right)\)
Ta thấy:
\(\frac{19}{29}< 1\Rightarrow\frac{19}{29}< \frac{19+1}{29+1}=\frac{20}{30}=\frac{2}{3}\)
Ta lại có:
\(\frac{2}{3}=\frac{2.7}{3.7}=\frac{14}{21}< 1\Rightarrow\frac{14}{21}< \frac{14+6}{21+6}=\frac{20}{27}=\frac{20.3}{27.3}=\frac{60}{81}\)
\(\Rightarrow\frac{19}{29}< \frac{60}{81}\) (1)
Ta có:
\(\frac{60}{81}=\frac{20}{27}< 1\Rightarrow\frac{20}{27}< \frac{20+1}{27+1}=\frac{21}{28}< \frac{21}{25}\)
=>\(\frac{60}{81}< \frac{21}{25}\) (2)
Từ (1) và (2) => \(\frac{19}{29}< \frac{60}{81}< \frac{21}{25}\)
\(\frac{21}{25}=\frac{49329}{58725}\)
\(\frac{60}{81}=\frac{43500}{58725}\)
\(\frac{19}{29}=\frac{38475}{58725}\)
\(\)vì \(\frac{49329}{58725}>\frac{43500}{58725}>\frac{38475}{58725}\)nên\(\frac{21}{25}>\frac{60}{81}>\frac{19}{29}\)
\(\frac{21}{25};\frac{60}{81};\frac{19}{29}\)
Ta có : \(\frac{60}{81}=\frac{60:3}{81:3}=\frac{20}{27}\); giữ nguyên \(\frac{21}{25};\frac{19}{29}\).
Vì \(\frac{21}{25}>\frac{20}{25}>\frac{20}{27}\)nên \(\frac{21}{25}>\frac{20}{27}\)
Vì \(\frac{20}{27}>\frac{20}{29}>\frac{19}{29}\)nên \(\frac{20}{27}>\frac{19}{29}\). Vậy :
\(\frac{21}{25}>\frac{20}{27}>\frac{19}{29}\)hay \(\frac{21}{25}>\frac{60}{81}>\frac{19}{29}\)
\(\frac{18}{75}=\frac{6}{25}\)
\(\frac{28}{112}=\frac{1}{4}=\frac{6}{24}\)
Vì 25>24 nên \(\frac{6}{25}< \frac{6}{24}\Leftrightarrow\frac{18}{75}>\frac{28}{112}\)
712/1425 < 461/920.