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\(\frac{7}{8}\)= \(\frac{1}{8}\)+ \(\frac{2}{8}\)+ \(\frac{4}{8}\)
\(\frac{7}{8}\)= \(\frac{2}{8}\)+ \(\frac{2}{8}\)+ \(\frac{3}{8}\)
\(1\)\(\frac{1}{2}\)=\(\frac{1+2}{2}\)=\(\frac{3}{2}\)=\(1,5\); \(2\frac{3}{5}\)=\(\frac{2\times5+3}{5}\)=\(\frac{13}{5}\)=\(2,6\)
\(3\frac{1}{4}\)=\(\frac{3\times4+1}{4}\)=\(\frac{13}{4}\)=\(3,25\) \(4\frac{7}{25}\)=\(\frac{4\times25+7}{25}\)=\(\frac{107}{25}\)=\(4,28\)
1/3-1/4 + 1/4-1/5 + 1/5-1/6 + 1/6-1/7 +...+ 1/11-1/12= 1/3-1/12 =1/4
\(\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+\frac{1}{5\cdot6}+\frac{1}{6\cdot7}+...+\frac{1}{11\cdot12}\)
\(=\left(\frac{1}{3}-\frac{1}{4}\right)+\left(\frac{1}{4}-\frac{1}{5}\right)+\left(\frac{1}{5}-\frac{1}{6}\right)+...+\left(\frac{1}{11}-\frac{1}{12}\right)\)
\(=\frac{1}{3}-\frac{1}{12}=\frac{1}{4}\)
96cm=96/100m=24/25m
72kg=72/1000 tấn =9/125 tấn
324m=324/1000km=81/250km
\(\frac{3}{4}=3:4;\frac{10}{3}=10:3;\frac{9}{5}=9:5;\frac{18}{2}=18:2;\frac{71}{100}=71:100\)
\(=\frac{1}{1x3}+\frac{1}{3x5}+\frac{1}{5x7}+...+\frac{1}{2013x2015}\)
\(=\frac{1}{2}x\left(\frac{2}{1x3}+\frac{2}{3x5}+\frac{2}{5x7}+...+\frac{2}{2013x2015}\right)\)
\(=\frac{1}{2}x\left(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{2013}-\frac{1}{2015}\right)\)
\(=\frac{1}{2}x\left(1-\frac{1}{2015}\right)\)
\(=\frac{1}{2}x\frac{2014}{2015}\)
\(=\frac{1007}{2015}\)
1/1-1/3+1/3-1/5+1/5-1/7+....+1/2013-1/2015
=1/1-1/2015
=2014/2015
4,89
4,89