Rút gọn phân số
25 . 12 + 25 . 17/ 29 . (-13) + 29 . (-27)
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a) \(\frac{12\cdot13}{5\cdot24}=\frac{13}{5\cdot2}=\frac{13}{10}\)
b)\(\frac{25\cdot17+25\cdot12}{29\cdot13+29\cdot14}=\frac{25\cdot\left(17+12\right)}{29\left(13+14\right)}=\frac{25\cdot29}{29\cdot27}=\frac{25}{27}\)
a, \(\frac{12.13}{5.24}=\frac{12.13}{5.2.12}=\frac{13}{10}\)
b, \(\frac{25.17+25.12}{29.13+29.14}=\frac{25.\left(17+12\right)}{29.\left(13+14\right)}=\frac{25.29}{29.27}=\frac{25}{27}\)
a: Phân số tối giản là 25/27; 77/79
b: 51/34=3/2
77/99=7/9
120/201=40/67
351/621=13/23
\(A=\frac{7}{10.11}+\frac{7}{11.12}+\frac{7}{12.13}+...+\frac{7}{69.70}\)
\(A=7\left(\frac{1}{10.11}+\frac{1}{11.12}+\frac{1}{12.13}+....+\frac{1}{69.70}\right)\)
\(A=7\left(\frac{1}{10}-\frac{1}{11}+\frac{1}{11}-\frac{1}{12}+....+\frac{1}{69}-\frac{1}{70}\right)\)
\(A=7\left(\frac{1}{10}-\frac{1}{70}\right)\)
\(A=7\cdot\frac{3}{35}=\frac{21}{35}\)
\(A=\frac{7}{10\cdot11}+\frac{7}{11\cdot12}+\frac{7}{12\cdot13}+...+\frac{7}{69\cdot70}\)
\(A=7\left(\frac{1}{10\cdot11}+\frac{1}{11\cdot12}+\frac{1}{12\cdot13}+...+\frac{1}{69\cdot70}\right)\)
\(A=7\left(\frac{1}{10}-\frac{1}{11}+\frac{1}{11}-\frac{1}{12}+...+\frac{1}{69}-\frac{1}{70}\right)\)
\(A=7\left(\frac{1}{10}-\frac{1}{70}\right)=7\cdot\frac{3}{35}=\frac{3}{5}\)
\(B=\frac{1}{25\cdot27}+\frac{1}{27\cdot29}+\frac{1}{29\cdot31}+...+\frac{1}{73\cdot75}\)
\(B=\frac{1}{2}\left(\frac{2}{25\cdot27}+\frac{2}{27\cdot29}+\frac{2}{29\cdot31}+...+\frac{2}{73\cdot75}\right)\)
\(B=\frac{1}{2}\left(\frac{1}{25}-\frac{1}{27}+\frac{1}{27}-\frac{1}{29}+...+\frac{1}{73}-\frac{1}{75}\right)\)
\(B=\frac{1}{2}\left(\frac{1}{25}-\frac{1}{75}\right)=\frac{1}{2}\cdot\frac{2}{75}=\frac{1}{75}\)
\(C=\frac{4}{2\cdot4}+\frac{4}{4\cdot6}+\frac{4}{6\cdot8}+...+\frac{4}{2008\cdot2010}\)
\(C=\frac{4}{2}\left(\frac{2}{2\cdot4}+\frac{2}{4\cdot6}+\frac{2}{6\cdot8}+...+\frac{2}{2008\cdot2010}\right)\)
\(C=2\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+...+\frac{1}{2008}-\frac{1}{2010}\right)\)
\(C=2\left(\frac{1}{2}-\frac{1}{2010}\right)=2\cdot\frac{502}{1005}=\frac{1004}{1005}\)
Gấp lắm ạ!
\(\dfrac{25.12+25.17}{29.\left(-13\right)+29.\left(-27\right)}=\dfrac{25.\left(12+17\right)}{29.\left[\left(-13\right)+\left(-17\right)\right]}=\dfrac{25.29}{29.\left(-30\right)}=\dfrac{725}{-870}\)