\(\dfrac{4}{27}+\dfrac{5}{9}+\dfrac{13}{9}-2\\ =\dfrac{4}{27}+\dfrac{18}{9}-2\\ =\dfrac{4}{27}+\dfrac{18\times3}{9\times3}-\dfrac{2\times27}{27}\\ =\dfrac{4}{27}+\dfrac{54}{27}-\dfrac{54}{27}\\ =\dfrac{4}{27}\)

`3/4+2/5+3/12`

`=3/4+3/12+2/5`

`=9/12+3/12+2/5`

`=12/12+2/5`

`=1+2/5`

`=7/5`

`7/13+5/9+6/13+5/9`

`=(7/13+6/13)+(5/9+5/9)`

`=13/13+10/9`

`=1+10/9`

`=9/9+10/9`

`=19/9`

19/9

21/11 × 22/17 × 68/63

= (21 × 2 × 4)/63

= 8/3

\(\dfrac{4}{7}x\left(\dfrac{2}{5}+\dfrac{3}{5}\right)=\dfrac{4}{7}x1=\dfrac{4}{7}\)

2/5 x 4/7 + 3/5 x 4/7

= (2/5 + 3/5 ) x 4/7

= 1 x 4/7

= 4/7

    2/5 *4/7+3/5*4/7

=( 2/5 + 3/5 ) *4/7 

= 1 * 4/7

= 4/7

\(=\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}\)

\(=\dfrac{1}{2}-\dfrac{1}{6}\)

\(=\dfrac{1}{3}\)

\(=\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}=\dfrac{1}{2}-\dfrac{1}{6}=\dfrac{1}{3}\)

`1/(2*3)+1/(3*4)+1/(4*5)+...+1/(9*10)`

`=1/2-1/3+1/3-1/4+1/4-1/5+...+1/9-1/10`

`=1/2-1/10`

`=5/10-1/10`

`=4/10=2/5`

\(=\dfrac{3}{7}\left(\dfrac{5}{4}-\dfrac{2}{9}\right)=\dfrac{3}{7}\cdot\dfrac{45-8}{36}=\dfrac{3}{36}\cdot\dfrac{37}{7}=\dfrac{37}{84}\)

\(\dfrac{3}{7}:\dfrac{4}{5}-\dfrac{3}{7}:\dfrac{9}{2}\)
\(=\dfrac{3}{7}\times\dfrac{5}{4}-\dfrac{3}{7}\times\dfrac{2}{9}\)
\(=\dfrac{3}{7}\times\left(\dfrac{5}{4}-\dfrac{2}{9}\right)\)
\(=\dfrac{3}{7}\times\left(\dfrac{45}{36}-\dfrac{8}{36}\right)\)
\(=\dfrac{3}{7}\times\dfrac{37}{36}\)
\(=\dfrac{37}{84}\)
#DatNe

 \(\dfrac{2}{3}\times\dfrac{3}{4}\times\dfrac{4}{5}\) \(=\dfrac{2\times3\times4}{3\times4\times5}\) \(=\) \(\dfrac{2}{5}\)

\(\dfrac{2}{3}x\dfrac{3}{4}x\dfrac{4}{5}=\dfrac{2}{5}\)

\(\dfrac{2}{3}\)x\(\dfrac{3}{5}\)^{=\(\dfrac{2}{5}\)}