Câu a:

(30 : 7\(\frac12\)) + 0,5 x 3 - 1,5) x(4\(\frac12\)-\(\frac92\)):(14,5 x 10)

= (30 :7\(\frac12\) + 0,5x3-1,5)x(\(\frac92\)-\(\frac92\)) : (14,5 x 10)

= (30:7\(\frac12\) + 0,5 x 3 - 1,5)x0 : (14,5 x 10)

= 0 :(14,5 x 10)

= 0

\(2009-\left(4\frac{5}{9}+x-7\frac{7}{18}\right):15\frac{2}{3}=2008\)

\(2009-\left(\frac{41}{9}+x-\frac{133}{18}\right):\frac{47}{3}=2008\)

\(\left(\frac{41}{9}+x-\frac{133}{18}\right):\frac{47}{3}=2009-2008\)

\(\left(\frac{41}{9}+x-\frac{133}{18}\right):\frac{47}{3}=1\)

\(\frac{41}{9}+x-\frac{133}{18}=1\cdot\frac{47}{3}\)

\(\frac{41}{9}+x-\frac{133}{18}=\frac{47}{3}\)

\(\frac{41}{9}+x=\frac{133}{18}+\frac{47}{3}\)

\(\frac{41}{9}+x=\frac{415}{18}\)

               \(x=\frac{415}{18}-\frac{41}{9}\)

                \(x=\frac{37}{2}\)

\(2009-\left(4\frac{5}{9}+x-7\frac{7}{18}\right)\div15\frac{2}{3}=2008\)

\(\left(4\frac{5}{9}+x-7\frac{7}{18}\right)\div15\frac{2}{3}=2009-2008\)

\(\left(-3\frac{3}{18}+x\right)\div15\frac{2}{3}=1\)

\(-3\frac{3}{18}+x=15\frac{2}{3}\)

\(x=15\frac{2}{3}+3\frac{3}{18}\)

\(x=15\frac{12}{18}+3\frac{3}{18}\)

\(x=18\frac{15}{18}\)

exactly 100%

\(\left(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+....+\frac{1}{2009\cdot2010}\right)\cdot x=2009\)

\(\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{2009}-\frac{1}{2010}\right)\cdot x=2009\)

\(\left(1-\frac{1}{2010}\right)\cdot x=2009\)

\(\frac{2009}{2010}\cdot x=2009\)

\(x=2009:\frac{2009}{2010}\)

\(x=2010\)

\(\left(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}+....+\frac{1}{2009}-\frac{1}{2010}\right).x=2009\)

\(\left(\frac{1}{1}-\frac{1}{2010}\right).x=2009\)

\(\frac{2009}{2010}.x=2009\)

\(x=2009:\frac{2009}{2010}\)

\(x=2010\)

a)\(\frac{27}{5}\text{x}\frac{91}{12}\text{x}\frac{125}{9}\text{x}\frac{96}{13}=\frac{27}{9}\text{x}\frac{91}{13}\text{x}\frac{125}{5}\text{x}\frac{96}{12}=3\text{x}7\text{x}25\text{x}8\)

Đến đây tự tính nha !

b)\(\frac{2539}{35}\text{x}\frac{7}{90}+\frac{561}{35}\text{x}\frac{7}{90}=\frac{7}{90}\text{x}\left(\frac{2539}{35}+\frac{561}{35}\right)=\frac{7}{90}\text{x}\frac{3100}{35}=\frac{3100}{90}\text{x}\frac{7}{35}=\frac{310}{9}\text{x}\frac{1}{5}=\frac{62}{9}\)

1. 27/5 x 91/12 x 125/9 x 96/13

2. 2539/35 x 7/90 + 561/35 x 7/90

3. 31/7 : (2/5 x 31/7)

4. (29 x 15/23 x 36/29) : 5/23

\(2009-\left(4\frac{5}{9}+x-7\frac{7}{8}\right):15\frac{3}{2}=2008\)

\(\Leftrightarrow2009-\left(\frac{41}{9}+x-\frac{63}{8}\right):\frac{33}{2}=2008\)

\(\Leftrightarrow2009-\left(x-\frac{239}{72}\right):\frac{33}{2}=2008\)

\(\Leftrightarrow2009-\frac{2x}{33}+\frac{239}{1188}=2008\)

\(\Leftrightarrow\frac{-2x}{33}=\frac{-1427}{1188}\)

\(\Leftrightarrow-2376x=-47091\)

\(\Leftrightarrow x=\frac{1427}{72}\)

ú chị to đi,

Dãy trên sẽ bằng: \(\frac{6}{5}\times\frac{7}{6}\times\frac{8}{7}\times........\times\frac{2010}{2009}\)

Sau đó rút gọn tử phân số này cho mẫu phân số kia thì được : \(\frac{2010}{5}=402\)

Chúc bạn học tốt!!!

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\(a,\)\(71+65\times4=\frac{x+140}{x}+260\)

\(\Rightarrow71+260=\frac{x-140}{x}+260\)

\(\Rightarrow71=\frac{x-140}{x}\)

\(\Rightarrow71x=x-140\)

\(\Rightarrow71x-x=-140\)

\(\Rightarrow70x=-140\)

\(\Rightarrow x=-2\)

\(b,\)\(y\times\frac{15}{2}-\frac{1}{3}\times\left(\frac{1}{4}+y\right)=90\frac{2}{3}\)

\(\Rightarrow\frac{15y}{2}-\frac{1}{12}-\frac{y}{3}=\frac{272}{3}\)

\(\Rightarrow\frac{90y}{12}-\frac{1}{12}-\frac{4y}{12}=\frac{1088}{12}\)

\(\Rightarrow90y-1-4y=1088\)

\(\Rightarrow86y=1089\)

\(\Rightarrow y=\frac{1089}{86}\)

y= 13,5

Trả lời:

\(y\times\frac{15}{2}-\frac{1}{3}\times\left(\frac{1}{4}+y\right)=96\frac{2}{3}\)

\(\Leftrightarrow y\times\frac{15}{2}-\frac{1}{12}-\frac{1}{3}\times y=\frac{290}{3}\)

\(\Leftrightarrow y\times\left(\frac{15}{2}-\frac{1}{3}\right)=\frac{387}{4}\)

\(\Leftrightarrow y\times\frac{43}{6}=\frac{387}{4}\)

\(\Leftrightarrow y=\frac{27}{2}\)

Vậy \(y=\frac{27}{2}\)

=> \(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{x.\left(x+1\right)}=\frac{2010}{2011}\)

=> \(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{x}-\frac{1}{x+1}=\frac{2010}{2011}\)

=>\(1-\frac{1}{x+1}=\frac{2010}{2011}\)

=> \(\frac{1}{x+1}=\frac{2011}{2011}-\frac{2010}{2011}=\frac{1}{2011}\)

=> x + 1 = 2011

=> x = 2010