a: \(=\dfrac{5}{14}\left(\dfrac{2}{9}+\dfrac{7}{9}+1\right)=\dfrac{5}{14}\cdot2=\dfrac{5}{7}\)

b: \(=\dfrac{6}{8}\left(\dfrac{6}{7}-6\right)=\dfrac{6}{8}\cdot\dfrac{-36}{7}=\dfrac{-216}{56}=\dfrac{-27}{7}\)

                   Đề Bài :\(\frac{9}{14}\)- \(\frac{x}{7}\): \(\frac{5}{3}\)= \(\frac{3}{14}\)

ta có : \(\frac{9}{14}\)- \(\frac{x}{7}\)= \(\frac{3}{14}\)x \(\frac{5}{3}\)= \(\frac{5}{14}\)

          \(\frac{x}{7}\)= \(\frac{9}{14}\)- \(\frac{5}{14}\)= \(\frac{4}{14}\)

         \(\frac{4}{14}\)= \(\frac{x}{7}\)=> \(\frac{4}{14}\)= \(\frac{2}{7}\)=> x = 2

\(\dfrac{9}{14}\times1+\dfrac{9}{14}\)

\(=\dfrac{9}{14}\times1+\dfrac{9}{14}\times1\)

\(=\dfrac{9}{14}\times\left(1+1\right)\)

\(=\dfrac{9}{14}\times2\)

\(=\dfrac{18}{14}=\dfrac{9}{7}\)

X × 14/9 - X × 5/9 = 13

X × (14/9 - 5/9) = 13

X × 1 = 13

X = 13

OEÊ

\(\dfrac{9}{14}\times13+\dfrac{9}{14}\)

\(=\dfrac{9}{14}\times13+\dfrac{9}{14}\times1\)

\(=\dfrac{9}{14}\times\left(13+1\right)\)

\(=\dfrac{9}{14}\times14\)

\(=\dfrac{126}{14}\) \(=9\)

\(2023\times0,8+2023\times9,2\)

\(=2023\times\left(0,8+9,2\right)\)

\(=2023\times10\)

\(=20230\)

\(\dfrac{9}{14}\times13+\dfrac{9}{14}\)

\(=\dfrac{117}{182}+\dfrac{9}{14}\)

\(=\dfrac{9}{7}\)

\(2023\times0,8+2023\times9,2\)

\(=2023\times\left(0,8+9,2\right)\)

\(=2023\times10\)

=\(20230\)

\(\dfrac{14}{9}\) x \(\dfrac{11}{8}-\dfrac{3}{8}\) x \(\dfrac{14}{9}\)

\(=\dfrac{14}{9}\) x \(\left(\dfrac{11}{8}-\dfrac{3}{8}\right)\)

\(=\dfrac{14}{9}\) x \(\dfrac{8}{8}=\dfrac{14}{9}\) x \(1\)

\(=\dfrac{14}{9}\)

oa cảm ơn bạn nhé :3

14/9 × 11/8 - 3/8 × 14/9 

= 14/9 × ( 11/8 - 3/8 ) 

= 14/9 × 8/8 

= 14/9 - 1 

= 5/9

\(\frac{9}{14}-\frac{x}{7}:\frac{5}{3}=\frac{3}{14}\Leftrightarrow\frac{9}{14}-\frac{3x}{35}=\frac{3}{14}\Leftrightarrow\frac{3x}{35}=\frac{3}{7}\Leftrightarrow3x=15\Leftrightarrow x=5\)

9/14-x/7:5/3=6/14

x/7:5/3=3/14

x/7=5/14

x=35/7

X = 35 thôi

 `-3/5xx9/14-3/5xx5/14+3/5`

`=(-3/5+3/5)xx(9/14+5/14)xx3/5`

`=0xx14xx3/5`

`=0xx1xx3/5`

`=0xx3/5`

`=0`

`@Nae`

\(-\dfrac{3}{5}\times\dfrac{9}{14}-\dfrac{3}{5}\times\dfrac{5}{14}+\dfrac{3}{5}\)

\(=\dfrac{3}{5}\times\left(-\dfrac{9}{14}-\dfrac{5}{14}+1\right)\)

\(=\dfrac{3}{5}\times\left(\dfrac{-9-5+14}{14}\right)\)

\(=\dfrac{3}{5}\times\dfrac{0}{14}\)

\(=0\)

\(\frac{1}{4\cdot9}+\frac{1}{9\cdot14}+\frac{1}{14\cdot19}+...+\frac{1}{1999+2004}\).

Có sai đề không vậy???

Sửa đề một chút :v

\(\frac{1}{4\cdot9}+\frac{1}{9\cdot14}+\frac{1}{14\cdot19}+...+\frac{1}{1999\cdot2004}\)

\(=\frac{1}{5}\left[\frac{5}{4\cdot9}+\frac{5}{9\cdot14}+\frac{5}{14\cdot19}+...+\frac{5}{1999\cdot2004}\right]\)

\(=\frac{1}{5}\left[\frac{1}{4}-\frac{1}{9}+\frac{1}{9}-\frac{1}{14}+...+\frac{1}{1999}-\frac{1}{2004}\right]\)

\(=\frac{1}{5}\left[\frac{1}{4}-\frac{1}{2004}\right]\)

\(=\frac{1}{5}\cdot\frac{125}{501}=\frac{25}{501}\)

Đặt A =1/4 x 9 + 1/9 x 14 + 1/14 x 19 +...+ 1/1999 + 2004. Ta có:

        A= 1/4 x 9 + 1/9 x 14 + 1/14 x 19 +...+ 1/1999 + 2004

      5A= 5/4 x 9 + 5/9 x 14 + 5/14 x 19 +...+ 5/1999 + 2004

      5A= 1/4 - 1/9 + 1/9 - 1/14 + 1/14 - 1/19 +...+ 1/1999 - 1/2004

      5A= 1/4 - 1/2004

        A= (1/4 - 1/2004)/5

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