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\(\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+...+\dfrac{1}{99\cdot100}\)
\(=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{99}-\dfrac{1}{100}\)
\(=1-\dfrac{1}{100}\)
\(=\dfrac{99}{100}\)
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3/17 x 4/21 + 3/17 x 25/21 - 8/21 x 3/17 = 3/17 x ( 4/21 + 25/21 - 8) = 3/17 x 1= 3/17
\(\frac{3}{17}.\frac{4}{21}+\frac{3}{17}.\frac{25}{21}-\frac{8}{21}.\frac{3}{17}\)
\(=\frac{3}{17}\left(\frac{4}{21}+\frac{25}{21}-\frac{8}{21}\right)\)
\(=\frac{3}{17}.1\)
\(=\frac{3}{17}\)
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\(\frac{5}{9}\times\frac{12}{7}=\frac{5\times12}{9\times7}=\frac{5\times4\times3}{3\times3\times7}=\frac{20}{21}\)
\(\frac{6}{5}:\frac{8}{3}=\frac{6}{5}\times\frac{8}{3}=\frac{2\times3\times8}{5\times3}=\frac{16}{5}\)
\(\frac{9}{20}\times\frac{5}{12}=\frac{3\times3\times5}{4\times5\times4\times3}=\frac{3}{16}\)
\(\frac{15}{16}:\frac{25}{24}=\frac{15}{16}\times\frac{24}{25}=\frac{3\times5\times4\times2\times3}{4\times2\times2\times5\times5}=\frac{9}{10}\)
\(14\times\frac{5}{21}=\frac{2\times7\times5}{3\times7}=\frac{10}{3}\)
\(10:\frac{5}{3}=10\times\frac{3}{5}=\frac{2\times5\times3}{5}=6\)
\(\frac{5}{3}:10=\frac{5}{3}\times\frac{1}{10}=\frac{5}{3\times2\times5}=\frac{1}{6}\)
\(\frac{21}{...\times3}=2\frac{1}{2}\)
\(\frac{21}{...\times3}=\frac{5}{2}\)
\(\frac{21\times5}{...\times3\times5}=\frac{5\times21}{2\times21}\) (qui đồng tử số)
=> ... x 3 x 5 = 2 x 21 = 42
=> ... = 42/15