121212/767676 =?
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\(\frac{121212}{151515}+\frac{121212}{353535}+\frac{121212}{636363}+\frac{121212}{999999}\)
= \(\frac{12.10101}{15.10101}+\frac{12.10101}{35.10101}+\frac{12.10101}{63.10101}+\frac{12.10101}{99.10101}\)
= \(\frac{12}{15}+\frac{12}{35}+\frac{12}{63}+\frac{12}{99}\)
= \(\frac{12}{3.5}+\frac{12}{5.7}+\frac{12}{7.9}+\frac{12}{9.11}\)
= \(6.\left(\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}\right)\)
= \(6.\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}\right)\)
= \(6.\left(\frac{1}{3}-\frac{1}{11}\right)\)
= \(6.\frac{8}{33}\)
= \(\frac{16}{11}\)
=\(70\left(\frac{121212}{565656}+\frac{121212}{727272}+\frac{121212}{909090}\right)\)
=\(70\left(\frac{3.40404}{14.40404}+\frac{121212}{6.121212}+\frac{2.60606}{15.60606}\right)\)
=\(70\left(\frac{3}{14}+\frac{1}{6}+\frac{2}{15}\right)\)
=\(70.\frac{18}{35}=38\)
\(\frac{767676}{252525}+\frac{2424}{2525}=\frac{76}{25}+\frac{24}{25}\)
\(=\frac{76+24}{25}=\frac{100}{25}=4\)
Ta có \(70\left(\frac{121212}{565656}+\frac{121212}{727272}+\frac{121212}{909090}\right)\)
\(=70\left(\frac{3\cdot40404}{14\cdot40404}+\frac{121212}{121212\cdot6}+\frac{2\cdot60606}{15\cdot60606}\right)\)
\(=70\left(\frac{3}{14}+\frac{1}{6}+\frac{2}{15}\right)\)
\(=70\cdot\frac{18}{35}=36\)
\(\dfrac{121212}{767676}=\dfrac{12}{76}=\dfrac{3}{19}\)
`121212/767676=(121212:40404)/(767676:40404)=3/19`