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\(5\dfrac{3}{4}:3+2\dfrac{1}{4}\times\dfrac{1}{3}-\dfrac{1}{8}=\left(5\dfrac{3}{4}+2\dfrac{1}{4}\right)\times\dfrac{1}{3}-\dfrac{1}{8}\\ =8\times\dfrac{1}{3}-\dfrac{1}{8}=\dfrac{8}{3}-\dfrac{1}{8}=\dfrac{61}{24}\\ ----\\ \dfrac{3}{5}:\dfrac{5}{6}:\dfrac{6}{7}:\dfrac{7}{8}+\dfrac{2}{5}+\dfrac{23}{35}\\ =\dfrac{3}{5}\times\dfrac{6}{5}\times\dfrac{7}{6}\times\dfrac{8}{7}+\dfrac{2}{5}+\dfrac{23}{35}=\dfrac{18}{25}\times\dfrac{4}{3}+\dfrac{2}{5}+\dfrac{23}{35}=\dfrac{353}{175}\)
\(\frac{1}{6}:\frac{4}{5}+\frac{1}{8}:\frac{4}{5}=\left(\frac{1}{6}+\frac{1}{8}\right):\frac{4}{5}=\left(\frac{4}{24}+\frac{3}{24}\right).\frac{5}{4}=\frac{7}{24}.\frac{5}{4}=\frac{35}{96}\)
\(\frac{1}{6}:\frac{4}{5}-\frac{1}{8}:\frac{4}{5}=\left(\frac{1}{6}-\frac{1}{8}\right):\frac{4}{5}=\left(\frac{4}{24}-\frac{3}{24}\right).\frac{5}{4}=\frac{1}{24}.\frac{5}{4}=\frac{5}{96}\)
a) 1/6 : 4/5 + 1/8 : 4/5 b) 1/6 : 4/5 - 1/8 : 4/5
= 4/5 : ( 1/6 + 1/8 ) = 4/5 : ( 1/6 - 1/8 )
= 4/5 : 7/24 = 4/5 : 1/24
= 96/35 = 96/5
`1/10+2/20+3/30+4/40+5/50+6/60+7/70+8/80+9/90`
`=1/10+1/10+1/10+1/10+1/10+1/10+1/10+1/10+1/10`
`=1/10xx9`
`=9/10`
\(1-\frac{1}{5}\times1-\frac{1}{6}\times.....\times1-\frac{1}{100}\)
\(=\frac{4}{5}\times\frac{5}{6}\times\frac{6}{7}\times\frac{7}{8}\times.....\times\frac{99}{100}\)
\(=\frac{4\times5\times....\times99}{5\times6\times...\times100}\)
\(=\frac{1}{25}\)
Ta có: \(\left(1-\frac{1}{5}\right)\left(1-\frac{1}{6}\right)\left(1-\frac{1}{7}\right)\left(1-\frac{1}{8}\right)...\left(1-\frac{1}{100}\right)\)
\(=\frac{4}{5}\cdot\frac{5}{6}\cdot\frac{6}{7}\cdot\frac{7}{8}\cdot...\cdot\frac{98}{99}\cdot\frac{99}{100}\)
\(=\frac{4}{100}=\frac{1}{25}\)