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\(\frac{1}{7}\times3\frac{1}{11}-\frac{1}{7}\times\frac{9}{11}-\frac{1}{7}\)
\(=\frac{1}{7}\times\frac{34}{11}-\frac{1}{7}\times\frac{9}{11}-\frac{1}{7}\)
\(=\frac{1}{7}\left(\frac{34}{11}-\frac{9}{11}-\frac{11}{11}\right)\)
\(=\frac{1}{7}\times\frac{14}{11}\)
\(=\frac{2}{11}\)
\(\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{9.10}\right).100-\left[\frac{5}{2}:\left(x+\frac{266}{100}\right)\right]:\frac{1}{2}=89\)
\(\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{9}-\frac{1}{10}\right).100-\left[\frac{5}{2}:\left(x+\frac{266}{100}\right)\right]:\frac{1}{2}=89\)
\(\left(1-\frac{1}{10}\right).100-\left[\frac{5}{2}:\left(x+\frac{266}{100}\right)\right]:\frac{1}{2}=89\)
\(90-\left[\frac{5}{2}:\left(x+\frac{266}{100}\right)\right]:\frac{1}{2}=89\)
\(\left[\frac{5}{2}:\left(x+\frac{266}{100}\right)\right]:\frac{1}{2}=1\)
\(\frac{5}{2}:\left(x+\frac{266}{100}\right)=\frac{1}{2}\Rightarrow x+\frac{266}{100}=5\Rightarrow x=\frac{117}{50}\)
Vậy x = 117/50
Ta có:
\(\left(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{9.10}\right).100\\ =\left(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{9}-\frac{1}{10}\right).100\)
\(=\left(1-\frac{1}{10}\right).100\)
\(=\frac{9}{10}.100\)
= 90
Khi đó đề bài sẽ thành : \(90-\left[\frac{5}{2}:\left(x+\frac{266}{100}\right)\right]:\frac{1}{2}=89\)
\(\Rightarrow\left[\frac{5}{2}:\left(x+\frac{266}{100}\right)\right]:\frac{1}{2}=1\)
\(\Rightarrow\frac{5}{2}:\left(x+\frac{266}{100}\right)=\frac{1}{2}\)
\(\Rightarrow x+\frac{266}{100}=5\)
\(\Rightarrow x=\frac{117}{50}\)
Vậy \(x=\frac{117}{50}\)
\(\left(1+\frac{1}{100}\right).\left(1+\frac{1}{99}\right)............\left(1+\frac{1}{2}\right)\)
\(=\frac{101}{100}.\frac{100}{99}..............\frac{3}{2}\)
\(=\frac{101.100............3}{100.99...............2}\)
\(=\frac{101}{2}\)
\(=\frac{101}{100}.\frac{100}{989}.....\frac{3}{2}=\frac{101}{2}\)
2x - \(\frac{2}{3}\)- \(\frac{3}{2}\)+ 3x = \(\frac{1}{2}\)
2x + 3x = \(\frac{1}{2}+\frac{2}{3}+\frac{3}{2}\)
5x = \(\frac{8}{3}\)
x = \(\frac{8}{3}:5\)
x = \(\frac{8}{15}\)
Cách này khó hiểu, có gì hỏi mình nhé
\(x\times\frac{1}{3}+x\times\frac{2}{3}=9\)
\(x\times\left(\frac{1}{3}+\frac{2}{3}\right)=9\)
\(x\times1=9\)
\(x=9\)
\(\frac{1}{3}.x+x.\frac{2}{3}=9\)
\(\Leftrightarrow x.\left(\frac{1}{3}+\frac{2}{3}\right)=9\)
\(\Leftrightarrow x.1=9\)
\(\Leftrightarrow x=9\)
=\(\frac{101}{2}\)
cac so triet tieu cho nhau roi \(=\frac{101}{100}\cdot\frac{100}{99}\cdot\frac{99}{98}\cdot.....\cdot\frac{4}{3}\cdot\frac{3}{2}\)
cac so tu 3 den 100 bi triet tieu
=\(\frac{101}{2}\)
\(\left(1+\frac{1}{100}\right).\left(1+\frac{1}{99}\right)...\left(1+\frac{1}{3}\right).\left(1+\frac{1}{2}\right)\)
\(=\frac{101}{100}.\frac{100}{99}...\frac{4}{3}.\frac{3}{2}\)
\(=\frac{101.\left(100...4.3\right)}{\left(100.99...3\right).2}\)
\(=\frac{101}{2}\)