\(\dfrac{2}{3}+\dfrac{7}{13}-\dfrac{17}{9}+\dfrac{19}{13}-\dfrac{1}{9}+\dfrac{7}{3}\)

\(=\left(\dfrac{2}{3}+\dfrac{7}{3}\right)+\left(\dfrac{7}{13}+\dfrac{19}{13}\right)-\left(\dfrac{17}{9}+\dfrac{1}{9}\right)\)

\(=\dfrac{9}{3}+\dfrac{26}{13}-\dfrac{18}{9}\)

\(=3+2-2\)

\(=3\)

a) \(19\times\left(52+38\right)-9\times\left(52+38\right)=\)

\(=\)     \(19\times90-9\times90\) 

\(=90\times\left(19-9\right)\) 

\(=90\times10\) 

\(=900\) 

b) \(\dfrac{2}{5}\div\dfrac{3}{7}\times\dfrac{3}{7}\div\dfrac{2}{5}+2019=\)

\(=\left(\dfrac{2}{5}\div\dfrac{2}{5}\right)\times\left(\dfrac{3}{7}\div\dfrac{3}{7}\right)+2019\) 

\(=1\times1+2019\) 

\(=2019\)

\(\dfrac{7}{19}\times\dfrac{1}{3}+\dfrac{7}{13}\times\dfrac{2}{3}\)

\(=\dfrac{7}{19}\times\left(\dfrac{1}{3}+\dfrac{2}{3}\right)\)

\(=\dfrac{7}{19}\times1\)

\(=\dfrac{7}{19}\)

19/37+1-19/37

=(19/37-19/37)+1

=0+1

=1

9/8-(17/7-3/7)+7/8

=(9/8+7/8)-(17/7-3/7)

=2-2

=0

1/2+3/4+1/2

=(1/2+1/2)+3/4

=1+3/4

=7/4

19/37 + 1 - 19/37 = (19/37 - 19/37) + 1 = 1

9/8 - (17/7 - 3/7) + 7/8 = (9/8 + 7/8) - (17/7 - 3/7) = 16/8 - 14/7 = 2 - 2 = 0

1/2 + 3/4 + 1/2 = (1/2 + 1/2) + 3/4 = 1 + 3/4 = 7/4

a, 19/37+1-19/37

= (19/37-19/37)+1

=1

b, 9/8- (17/7-3/7)+7/8

= (9/8+7/8) - (17/7-3/7)

=16/8 - 14/7

= 2 - 2

=0

c, 1/2+3/4+1/2

= (1/2+1/2)+3/4

=1+3/4

=7/4

\(\dfrac{3}{11}\text{×}\dfrac{7}{19}+\dfrac{3}{11}\text{×}\dfrac{10}{19}+\dfrac{3}{11}\text{×}\dfrac{1}{19}=\dfrac{3}{11}\text{×}\left(\dfrac{7}{19}+\dfrac{10}{19}+\dfrac{2}{19}\right)=\dfrac{3}{11}\text{×}1=\dfrac{3}{11}\)

\(\frac{3}{7}x\frac{25}{19}-\frac{1}{7}x\frac{18}{19}\)

\(=\left(\frac{3}{7}-\frac{1}{7}\right)x\left(\frac{25}{19}-\frac{18}{19}\right)\)

\(=\frac{2}{7}x\frac{7}{19}\)

\(=\frac{14}{133}\)

3/7×25/19-2/7×18/19

75/133-36-133

39/133

\(\left(\dfrac{2}{7}+\dfrac{5}{7}\right)+\left(\dfrac{3}{5}+\dfrac{2}{5}\right)+\left(\dfrac{3}{8}+\dfrac{4}{8}+\dfrac{1}{8}\right)+\left(\dfrac{1}{9}+\dfrac{8}{9}\right)=1+1+1+1=4\)

(2/7 + 5/7) + (3/5 + 2/5) + (3/8 + 4/8 + 1/8) + (1/9 + 8/9 )

= 1  +       1                   +         1             +        1         =  4

\(\left(a\right)\frac{3}{5}\cdot\frac{8}{21}\cdot\frac{5}{3}=\left(\frac{3}{5}\cdot\frac{5}{3}\right)\cdot\frac{8}{21}=1\cdot\frac{8}{21}=\frac{8}{21}\)

(b) sai đề

\(\left(c\right)x\cdot\frac{1}{2}=\frac{1}{3}\)

\(x=\frac{\frac{1}{3}}{\frac{1}{2}}=\frac{2}{3}\)

\(\left(d\right)\frac{x}{\frac{4}{5}}=\frac{5}{2}\)

\(x=\frac{5}{2}\cdot\frac{4}{5}=2\)

\(\left(e\right)\frac{\frac{2}{9}}{x}=\frac{2}{3}\)

\(x=\frac{\frac{2}{9}}{\frac{2}{3}}=\frac{1}{3}\)