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Mình trình bày trong hình nhé ^^ Bn tham khảo ạ\(3\dfrac{2}{5}\cdot1\dfrac{4}{7}=\dfrac{17}{5}\cdot\dfrac{11}{7}=\dfrac{187}{35}\)
a) \(\frac{51}{3}-\frac{22}{3}=\frac{51-22}{3}=\frac{29}{3}\)
b) \(\frac{5}{12}+\frac{5}{6}-\frac{3}{4}=\frac{5}{12}+\frac{10}{12}-\frac{9}{12}=\frac{5+10-9}{12}=\frac{6}{12}=\frac{1}{2}\)
c) \(1-\left(\frac{1}{5}+\frac{1}{2}\right)=\frac{10}{10}-\frac{2}{10}-\frac{5}{10}=\frac{10-5-2}{10}=\frac{3}{10}\)
d) \(\frac{111}{4}-\left(\frac{25}{7}+\frac{51}{4}\right)=\frac{777}{28}-\frac{60}{28}-\frac{357}{28}=\frac{360}{28}=\frac{90}{7}\)
e) \(\left(\frac{85}{11}+\frac{35}{7}\right)-\frac{35}{11}=\left(\frac{85}{11}-\frac{35}{11}\right)+\frac{35}{7}=\frac{50}{11}-\frac{35}{7}=\frac{350}{77}-\frac{385}{77}=-\frac{35}{77}\)
Đặt A = \(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+.....+\frac{1}{17.19}\)
\(\Rightarrow2A=\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+.....+\frac{2}{17.19}\)
\(\Rightarrow2A=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+.....+\frac{1}{17}-\frac{1}{19}\)
\(\Rightarrow2A=1-\frac{1}{19}\)
\(\Rightarrow2A=\frac{18}{19}\)
\(\Rightarrow A=\frac{18}{19}.\frac{1}{2}=\frac{9}{19}\)
\(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{17.19}\)
\(=\frac{1}{2}.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{17}-\frac{1}{19}\right)\)
\(=\frac{1}{2}.\left(1-\frac{1}{19}\right)\)
\(=\frac{1}{2}.\frac{18}{19}=\frac{9}{19}\)
\(D=\frac{5}{1+2+3}+\frac{5}{1+2+3+4}+...+\frac{5}{1+2+...+100}\)
\(\Rightarrow D=5\left(\frac{1}{1+2+3}+\frac{1}{1+2+3+4}+...+\frac{1}{1+2+...+100}\right)\)
\(\Rightarrow D=5\left(\frac{1}{\frac{4.3}{2}}+\frac{1}{\frac{5.4}{2}}+...+\frac{1}{\frac{101.100}{2}}\right)\)
\(\Rightarrow D=5\left(\frac{2}{3.4}+\frac{2}{4.5}+...+\frac{2}{100.101}\right)\)
\(\Rightarrow D=10\left(\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{100}-\frac{1}{101}\right)\)
\(\Rightarrow D=10\left(\frac{1}{3}-\frac{1}{101}\right)\)
\(\Rightarrow D=\frac{10}{3}-\frac{10}{101}=\frac{980}{303}\)
I don't now
or no I don't
..................
sorry
=17/6:(1-2/3)
=17/6:1/3
=17/2
=13/6×9/2-6/7
=39/4-6/7
=249/28
a) \(\left(\frac{5}{2}+\frac{1}{3}\right):\left(1-\frac{2}{3}\right)=\left(\frac{15}{6}+\frac{2}{6}\right):\frac{1}{3}\)
\(=\frac{17}{6}:\frac{1}{3}=\frac{17}{6}\cdot\frac{3}{1}=\frac{17}{2}\cdot\frac{1}{1}=\frac{17}{2}\)
b) \(\left(\frac{5}{2}-\frac{1}{3}\right)\cdot\frac{9}{2}-\frac{6}{7}=\left(\frac{15}{6}-\frac{2}{6}\right)\cdot\frac{9}{2}-\frac{6}{7}\)
\(=\frac{13}{6}\cdot\frac{9}{2}-\frac{6}{7}=\frac{13}{2}\cdot\frac{3}{2}-\frac{6}{7}=\frac{39}{4}-\frac{6}{7}=\frac{273}{28}-\frac{24}{28}=\frac{249}{28}\)