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\(\frac{1}{2}+\frac{1}{2}=\frac{1+1}{2}=\frac{2}{2}=1\)
\(\frac{3}{4}+\frac{1}{4}=\frac{3+1}{4}=\frac{4}{4}=1\)
\(\frac{3}{9}+\frac{6}{9}=\frac{3+6}{9}=\frac{9}{9}=1\)

\(\frac{1}{2}:\frac{3}{2}:\frac{5}{4}:\frac{6}{5}:\frac{7}{6}:\frac{8}{7}\)
\(=\frac{1}{2}\cdot\frac{2}{3}\cdot\frac{4}{5}\cdot\frac{5}{6}\cdot\frac{6}{7}\cdot\frac{7}{8}\)
\(=\frac{1\cdot\left(2\cdot5\cdot6\cdot7\right)}{8\cdot3\cdot\left(2\cdot5\cdot6\cdot7\right)}\)
\(=\frac{1}{24}\)
\(\frac{1}{2}\cdot\frac{2}{3}\cdot\frac{3}{4}\cdot\frac{4}{5}\cdot\frac{5}{6}\cdot\frac{6}{7}\cdot\frac{7}{8}\cdot\frac{8}{9}\cdot\frac{9}{10}\)
\(=\frac{1\cdot\left(2\cdot3\cdot4\cdot5\cdot6\cdot7\cdot8\cdot9\right)}{\left(2\cdot3\cdot4\cdot5\cdot6\cdot7\cdot8\cdot9\right)\cdot10}\)
\(=\frac{1}{10}\)

Tính nhanh:
\(\frac{1}{1}+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\)\(\frac{1}{5}+\frac{1}{6}+\frac{1}{7}+\frac{1}{8}+\frac{1}{9}\)
\(=\left(\frac{1}{1}+\frac{1}{9}\right)+\left(\frac{1}{2}+\frac{1}{8}\right)\)\(+\left(\frac{1}{3}+\frac{1}{7}\right)+\left(\frac{1}{4}+\frac{1}{6}\right)+\frac{1}{5}\)
\(=\frac{1}{10}+\frac{1}{10}+\frac{1}{10}+\frac{1}{10}+\frac{1}{5}\)
\(=\frac{4}{10}+\frac{2}{5}=\frac{2}{5}+\frac{1}{5}=\frac{3}{5}\)
tks giúp mk nha! cảm ơn nhiều ạ...
Đặt \(A=2-1+1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-...-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}\)
\(=2-\frac{1}{9}=\frac{18}{9}-\frac{1}{9}=\frac{17}{9}\)

Ta có:
\(\left(1-\frac{1}{11}\right)\times\left(1-\frac{1}{10}\right)\times\left(1-\frac{1}{9}\right)\times\left(1-\frac{1}{8}\right)\times\left(1-\frac{1}{7}\right)\times\left(1-\frac{1}{6}\right)\)
\(=\frac{10}{11}\times\frac{9}{10}\times\frac{8}{9}\times\frac{7}{8}\times\frac{6}{7}\times\frac{5}{6}\)
\(=\frac{10\times9\times8\times7\times6\times5}{11\times10\times9\times8\times7\times6}\)
\(=\frac{5}{11}\)

\(a,\frac{3}{15}+\frac{2}{5}=\frac{1}{5}+\frac{2}{5}=\frac{3}{5}.\)
\(b,\frac{9}{8}-\frac{5}{6}=\frac{7}{24}\)
\(c,\frac{1}{2}+\frac{3}{7}+\frac{11}{14}=\frac{13}{14}+\frac{11}{14}=\frac{24}{14}=\frac{12}{7}\)
\(d,\frac{8}{3}-\frac{1}{2}-1=\frac{13}{6}-1=\frac{7}{6}\)
~~~ học tốt ~~~

a/ \(\left[\frac{4}{6}+\frac{14}{6}\right]+\left[\frac{7}{13}+\frac{19}{13}\right]+\left[\frac{17}{9}+\frac{1}{9}\right]=\frac{18}{6}+\frac{26}{13}+\frac{18}{9}=3+2+2=7\)

\(\frac{1}{6}+\frac{5}{6}=\frac{6}{6}=1\)
\(\frac{25}{5}+\frac{2}{6}=\frac{150}{30}+\frac{10}{30}=\frac{160}{30}=\frac{32}{6}=\frac{16}{3}\)
\(\frac{12}{5}+\frac{6}{9}=\frac{108}{45}+\frac{30}{45}=\frac{138}{45}\)
\(\frac{1}{2}+\frac{1}{6}+\frac{1}{9}=\frac{9}{18}+\frac{3}{18}+\frac{2}{18}=\frac{14}{18}=\frac{7}{9}\)
1/2 + 1/6 + 1/9
= ( 1/2 + 1/6 ) + 1/9
= ( 3/6 + 1/6 ) + 1/9
= 4/6 + 1/9
= 2/3 + 1/9
= 6/9 + 1/9
= 7/9