\(\frac{2}{5}:\frac{1}{3}-\frac{2}{15}:\frac{1}{5}+\frac{3}{5}.\frac{1}{3}\)

\(=\frac{6}{5}+\frac{-2}{3}+\frac{1}{5}\)

\(=\frac{11}{15}\)

~ Hok tốt ~

\(\frac{4}{2.4}+\frac{4}{4.6}+\frac{4}{6.8}+...+\frac{4}{2008.2010}\)

\(=4.\left(\frac{1}{2.4}+\frac{1}{4.6}+\frac{1}{6.8}+...+\frac{1}{2008.2010}\right)\)

\(=4.\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{2008}-\frac{1}{2010}\right)\)

\(=4.\left[\frac{1}{2}+\left(\frac{1}{4}-\frac{1}{4}\right)+\left(\frac{1}{6}-\frac{1}{6}\right)+\left(\frac{1}{8}-\frac{1}{8}\right)+...+\left(\frac{1}{2008}-\frac{1}{2008}\right)-\frac{1}{2010}\right]\)

\(=4.\left[\frac{1}{2}-\frac{1}{2010}\right]\)

\(=4.\frac{502}{1005}=\frac{2008}{1005}\)

~ Hok tốt ~

b, \(\frac{4}{2.4}+\frac{4}{4.6}+\frac{4}{6.8}+...+\frac{4}{2008.2010}\)

\(=2\left(\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+...+\frac{2}{2008.2010}\right)\)

\(=2\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{2008}-\frac{1}{2010}\right)\)

\(=2\left(\frac{1}{2}-\frac{1}{2010}\right)\)

\(=2.\frac{502}{1005}\)

\(=\frac{1004}{1005}\)

Study well ! >_<

\(a,\frac{1}{3}x+\frac{2}{5}x-\frac{2}{5}=0\)

\(\frac{11}{15}x=\frac{2}{5}\)

\(x=\frac{6}{11}\)

b,\(\left(2x-3\right).\left(6-2x\right)=0\)

\(\Rightarrow\orbr{\begin{cases}2x-3=0\\6-2x=0\end{cases}\Rightarrow}\orbr{\begin{cases}x=\frac{3}{2}\\x=3\end{cases}}\)

Vậy

\(\left(3x-1\right).\left(-\frac{1}{2}x+5\right)=0\)
\(\Rightarrow\orbr{\begin{cases}3x-1=0\\-\frac{1}{2}x+5=0\end{cases}\Rightarrow\orbr{\begin{cases}x=\frac{1}{3}\\x=10\end{cases}}}\)\

Vậy

dễ mà bạn làm từ câu a nếu ra thì các câu khác cũng dễ thôi

\(A=\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+....+\frac{1}{2009\cdot2010}\)

\(A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{2009}-\frac{1}{2010}\)

\(A=1-\frac{1}{2010}\)

\(A=\frac{2009}{2010}\)

K:2=2/2.4+2/4.6+2/6.8+...+2/2008.2010

     =1/2-1/4+1/4-1/6+1/6-1/8+...+1/2008-1/2010

     =1/2-1/2010

     =502/1005

  K=502/1005.2

    =1004/1005

F=1/3.6+1/6.9+1/9.12+...+1/30.33

3F=3/3.6+3/6.9+3/9.12+...+1/30.33

    =1/3-1/6+1/6-1/9+1/9-1/12+...+1/30-1/33

    =1/3-1-33

    =10/33

  F=10/33:3

    =10/99

Bn sai câu K = 4/2.4 + 4/4.6 + 4/6.8 +....+ 4/2008.2010 

Ko biết làm

a: \(=\dfrac{3\left(\dfrac{1}{41}-\dfrac{4}{47}+\dfrac{9}{53}\right)}{4\left(\dfrac{1}{47}-\dfrac{4}{47}+\dfrac{9}{53}\right)}=\dfrac{3}{4}\)

b: \(F=2\left(\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{6}+...+\dfrac{1}{2008}-\dfrac{1}{2010}\right)\)

\(=2\cdot\dfrac{1004}{2010}=\dfrac{2008}{2010}=\dfrac{1004}{1005}\)

c: \(S=\dfrac{1}{3\cdot6}+\dfrac{1}{6\cdot9}+...+\dfrac{1}{30\cdot33}\)

\(=\dfrac{1}{3}\left(\dfrac{1}{3}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{9}+...+\dfrac{1}{30}-\dfrac{1}{33}\right)\)

\(=\dfrac{1}{3}\cdot\dfrac{10}{33}=\dfrac{10}{99}\)

\(b,C=\dfrac{1}{18}+\dfrac{1}{54}+\dfrac{1}{108}+...+\dfrac{1}{990}\\ =\dfrac{1}{3.6}+\dfrac{1}{6.9}+\dfrac{1}{9.12}+...+\dfrac{1}{30.33}\\ =\dfrac{1}{3}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{12}+...+\dfrac{1}{30}-\dfrac{1}{33}\\ =\dfrac{1}{3}-\dfrac{1}{33}\\ =\dfrac{11}{33}-\dfrac{1}{33}=\dfrac{10}{33}\)

a.F=\(\dfrac{4}{2.4}\)+\(\dfrac{4}{4.6}\)+\(\dfrac{4}{6.8}\)+...+\(\dfrac{4}{2008.2010}\)

F=\(\dfrac{2.2}{2.4}\)+\(\dfrac{2.2}{4.6}\)+\(\dfrac{2.2}{6.8}\)+...+\(\dfrac{2.2}{2008.2010}\)

F=2.(\(\dfrac{2}{2.4}\)+\(\dfrac{2}{4.6}\)+\(\dfrac{2}{6.8}\)+...+\(\dfrac{2}{2008.2010}\))

F=2.(\(\dfrac{1}{2}\)-\(\dfrac{1}{4}\)+\(\dfrac{1}{4}\)-\(\dfrac{1}{6}\)+\(\dfrac{1}{6}\)-\(\dfrac{1}{8}\)+...+\(\dfrac{1}{2008}\)-\(\dfrac{1}{2010}\))

F=2.(\(\dfrac{1}{2}\)-\(\dfrac{1}{2010}\))

F=\(\dfrac{1004}{1005}\)

b, C=\(\dfrac{1}{18}\)+\(\dfrac{1}{54}\)+....+\(\dfrac{1}{990}\)

\(\Rightarrow\)C=\(\dfrac{1}{3.6}\)+\(\dfrac{1}{6.9}\)+...+\(\dfrac{1}{30.33}\)

=>3C=3( \(\dfrac{1}{3.6}\)+\(\dfrac{1}{6.9}\)+...+\(\dfrac{1}{30.33}\))

=>3C=\(\dfrac{3}{3.6}\)+\(\dfrac{3}{6.9}\)+....+\(\dfrac{3}{30.33}\)

=> 3C=\(\dfrac{1}{3}\)-\(\dfrac{1}{6}\)+\(\dfrac{1}{6}\)-\(\dfrac{1}{9}\)+...+\(\dfrac{1}{30}\)-\(\dfrac{1}{33}\)

=> 3C= \(\dfrac{1}{3}\)-\(\dfrac{1}{33}\)

=>3C=\(\dfrac{10}{33}\)

=> C=\(\dfrac{10}{33}\):3

=> C=\(\dfrac{10}{99}\)

a, F=4/2.4+4/4/6+4/6.8+......+4/2008.2010

=> F= 4/2.(2/2.4+2/4.6+2/6.8+......+2/2008/2010

=> F= 4/2. ( 1/2-1/4+1/4-1/6+1/6-1/8+......+1/2008-1/2010

=> F=4/2.( 1/2-1/2010)

=> F= 4/2. 502/1005

=> F= \(\dfrac{1004}{1005}\)

\(A=\frac{4}{2.4}+\frac{4}{4.6}+\frac{4}{6.8}+.....+\frac{4}{2008.2010}\)

\(\Rightarrow A=4\left(\frac{1}{2.4}+\frac{1}{4.6}+\frac{1}{6.8}+.....+\frac{1}{2008.2010}\right)\)

\(\Rightarrow A=4\left[\frac{1}{2}\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+....+\frac{1}{2008}-\frac{1}{2010}\right)\right]\)

\(\Rightarrow A=4\left[\frac{1}{2}\left(\frac{1}{2}-\frac{1}{2010}\right)\right]\Rightarrow A=4\left(\frac{1}{2}.\frac{502}{1005}\right)\Rightarrow A=4.\frac{251}{1005}\Rightarrow A=\frac{1004}{1005}\)

\(B=\frac{1}{18}+\frac{1}{54}+\frac{1}{108}+....+\frac{1}{990}\)

\(\Rightarrow B=\frac{1}{3.6}+\frac{1}{6.9}+\frac{1}{9.12}+....+\frac{1}{30.33}\)

\(\Rightarrow B=\frac{1}{3}\left(\frac{1}{3}-\frac{1}{6}+\frac{1}{6}-\frac{1}{9}+\frac{1}{9}-\frac{1}{12}+.....+\frac{1}{30}-\frac{1}{33}\right)\)

\(\Rightarrow B=\frac{1}{3}.\left(\frac{1}{3}-\frac{1}{33}\right)\Rightarrow B=\frac{1}{3}.\frac{10}{33}\Rightarrow B=\frac{10}{99}\)

= 2(2/2.4 + 2/4.6 +.....+ 2/2008.2016)

= 2(1/2 - 1/4 + 1/4 - 1/6 +....+ 1/2008 - 1/2016)

= 2(1/2 - 1/2016)

=2 . 1007/2016

=1007/1008

                                                                         Bài làm

1.

11 3/13 - ( 2 4/7 + 5 3/13 )

= 11 3/13 - 2 4/7 - 5 3/13

= ( 11 3/13 - 5 3/13 ) - 2 4/7

= { (11 - 5 ) . ( 3/13 - 3/13 ) } - 2 4/7

= ( 6 . 0 ) - 2 4/7

= 0 - 2 4/7

= 2 4/7

= 18/7

2 .

19 5/8 : 7/12 + ( -15 1/4) : 7/12

= { 19 5/8 + ( -15 1/4 ) } : 7/12

= [ { 19 + ( - 15) } . ( 5/8 + 1/4 ) ] : 7/12

= { 4 . ( 5/8 + 2/8 ) } : 7/12

= ( 4 . 7/8 ) : 7/12

= 1.7/2 : 7/12

= 7/2 : 7/12

= 7/2 . 12/7

= 1.1/6.1

= 1/6

3 .

2/5 . 1/3 - 2 2/15 : 1/5 + 3/5 . 1/3

= 1/3 . ( 2/5 + 3/5 ) - 2 2/15 : 1/5

= 1/3 . 5/5 - 32/15 . 5/1

= 1/3 . 1 - 32.1/3.1

= 1/3 - 32/3

= -31/3

4 .

( 3 1/3 + 2,5 ) : ( 3 1/6 - 4 1/5 ) - 11/31

= ( 10/3 + 25/10 ) : { ( 3 - 4 ) . ( 1/6 - 1/5 ) - 11/31

= ( 10/3 + 5/2 ) : { (-1) . ( 5/30 - 6/30 ) } - 11/31

= ( 20/6 + 15/6 ) : { (-1) . (-1)/30 } - 11/31

= 35/6 : 1/30 - 11/31

= 35/6 . 30/1 - 11/31

= 35.5/1.1 - 11/31

= 175 - 11/31

= 5425/31 - 11/31

= 5414/31

5.

75% - 1 1/5 + 0,5 : 5/12 - (-1/2)²

= 75/100 - 6/5 + 5/12 - 1/4

= 3/4 - 6/5 + 5/12 - 1/4

= ( 3/4 - 1/4 ) + ( 5/12 - 6/5 )

= 2/4 + ( 25/60 - 30/60 )

= 1/2 + (-5)/60

= 1/2 + (-1)/12

= 6/12 + (-1)/12

= 5/12

Đúng thì k cho mình nha !

1)

11 3/13 - ( 2 4/7 + 5 3/13 )

= 11 3/13 - 2 4/7 - 5 3/13

= ( 11 3/13 - 5 3/13 ) - 2 4/7

= { (11 - 5 ) . ( 3/13 - 3/13 ) } - 2 4/7

= ( 6 . 0 ) - 2 4/7

= 0 - 2 4/7

= 2 4/7

= 18/7

2 )

19 5/8 : 7/12 + ( -15 1/4) : 7/12

= { 19 5/8 + ( -15 1/4 ) } : 7/12

= [ { 19 + ( - 15) } . ( 5/8 + 1/4 ) ] : 7/12

= { 4 . ( 5/8 + 2/8 ) } : 7/12

= ( 4 . 7/8 ) : 7/12

= 1.7/2 : 7/12

= 7/2 : 7/12

= 7/2 . 12/7

= 1.1/6.1

= 1/6

3 )

2/5 . 1/3 - 2 2/15 : 1/5 + 3/5 . 1/3

= 1/3 . ( 2/5 + 3/5 ) - 2 2/15 : 1/5

= 1/3 . 5/5 - 32/15 . 5/1

= 1/3 . 1 - 32.1/3.1

= 1/3 - 32/3

= -31/3

4 )

( 3 1/3 + 2,5 ) : ( 3 1/6 - 4 1/5 ) - 11/31

= ( 10/3 + 25/10 ) : { ( 3 - 4 ) . ( 1/6 - 1/5 ) - 11/31

= ( 10/3 + 5/2 ) : { (-1) . ( 5/30 - 6/30 ) } - 11/31

= ( 20/6 + 15/6 ) : { (-1) . (-1)/30 } - 11/31

= 35/6 : 1/30 - 11/31

= 35/6 . 30/1 - 11/31

= 35.5/1.1 - 11/31

= 175 - 11/31

= 5425/31 - 11/31

= 5414/31

5)

75% - 1 1/5 + 0,5 : 5/12 - (-1/2)²

= 75/100 - 6/5 + 5/12 - 1/4

= 3/4 - 6/5 + 5/12 - 1/4

= ( 3/4 - 1/4 ) + ( 5/12 - 6/5 )

= 2/4 + ( 25/60 - 30/60 )

= 1/2 + (-5)/60

= 1/2 + (-1)/12

= 6/12 + (-1)/12

= 5/12

1=18/7

2=1/6

3=31/3

4=5414/31

5=5/12