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Ta có : \(\frac{969696}{979797}=\frac{969696:10101}{979797:10101}=\frac{96}{97}\left(1\right)\)
\(\frac{123123123}{124124124}=\frac{123123123:1001001}{124124124:1001001}=\frac{123}{124}\left(2\right)\)
Lại có : \(\frac{96}{97}=1-\frac{1}{97}\)
\(\frac{123}{124}=1-\frac{1}{124}\)
Mà \(\frac{1}{97}>\frac{1}{124}\) nên \(\frac{96}{97}< \frac{123}{124}\)
Hay \(\frac{969696}{979797}< \frac{123123123}{124124124}\)
\(\frac{121212}{151515}+\frac{121212}{353535}+\frac{121212}{636363}+\frac{121212}{999999}\)
= \(\frac{12.10101}{15.10101}+\frac{12.10101}{35.10101}+\frac{12.10101}{63.10101}+\frac{12.10101}{99.10101}\)
= \(\frac{12}{15}+\frac{12}{35}+\frac{12}{63}+\frac{12}{99}\)
= \(\frac{12}{3.5}+\frac{12}{5.7}+\frac{12}{7.9}+\frac{12}{9.11}\)
= \(6.\left(\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}\right)\)
= \(6.\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}\right)\)
= \(6.\left(\frac{1}{3}-\frac{1}{11}\right)\)
= \(6.\frac{8}{33}\)
= \(\frac{16}{11}\)
\(\frac{131313}{151515}+\frac{131313}{353535}+\frac{131313}{636363}+\frac{131313}{999999}\)
\(=\frac{13}{15}+\frac{13}{35}+\frac{13}{63}+\frac{13}{99}\)
\(=13.\left(\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+\frac{1}{99}\right)\)
\(=13.\left(\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+\frac{1}{9.11}\right)\)
\(=13.\)\(\frac{1}{2}.\left(\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}\right)\)
\(=\frac{13}{2}.\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-...-\frac{1}{11}\right)\)
\(=\frac{13}{2}.\left(\frac{1}{3}-\frac{1}{11}\right)\)
\(=\frac{13}{2}.\frac{8}{33}\)
\(=\frac{52}{33}\)
!
202020/454545
= 20/45
= 4/9
~~tk mk nha m.n và Trần Thị Anh Thư ~^^
Ai Tk mK ThÌ mK tK LạI NhA ~~~~~~~~~~~~~~~~~~~~~~~~~~~~^^
\(\frac{424242}{303030}\) = \(\frac{424242:60606}{303030:60606}\) = \(\frac{7}{5}\)
121212/969696 = 12/96 303030/454545 = 30/45
rút gọn tối giản rồi quy đồng
121212/969696<303030/454545