`7/13 . 5/19 + 7/19 . 8/13 - 3 . 7/19`

`=7/13 . 5/19 + 7/19 . (  8/13 - 3)`

`=7/13 . 5/19 + 7/19 . ( 8/13- 39/13)`

`=7/13 . 5/19 + 7/19 . (-31/13)`

`= 35/247 + (-217)/247`

`=-14/19`

`A=-1/6 . 3/2 . (-12)`

`= -3/12 . (-12)`

`=-1/4 . (-12)`

`= 12/4`

`=3`

\(A=-\dfrac{1}{6}\cdot\dfrac{3}{2}\cdot\left(-12\right)\)
\(=-\dfrac{1}{4}\cdot-12\)
\(=3\)

`(4 +3/5) . 17/8 +(2+7/8) : 5/23`

`= (20/5 + 3/5) . 17/8 +( 16/8+7/8) . 23/5`

`= 23/5 . 17/8 + 23/8 . 23/5`

`= 23/5. (17/8+23/8)`

`=23/5 . 5`

`=115/5`

`=23`

\(\left(\dfrac{2}{3}\cdot\dfrac{7}{5}-\dfrac{2}{5}\cdot\dfrac{2}{3}\right):\left(-\dfrac{1}{6}+\dfrac{10}{12}\right)\)
\(=\left(\dfrac{2}{3}\cdot\dfrac{7}{5}-\dfrac{2}{3}\cdot\dfrac{2}{5}\right):\left(-\dfrac{1}{6}+\dfrac{5}{6}\right)\)
\(=\dfrac{2}{3}\cdot\left(\dfrac{7}{5}-\dfrac{2}{5}\right):\left(-\dfrac{4}{6}\right)\)
\(=\dfrac{2}{3}\cdot1\cdot-\dfrac{3}{2}\)
\(=-\dfrac{2.3}{3.2}\)
\(=-1\)

\(-\dfrac{3}{5}\cdot\dfrac{4}{9}+\dfrac{3}{-5}\cdot\dfrac{14}{9}+\dfrac{1}{5}\)
\(=-\dfrac{3}{5}\cdot\left(\dfrac{4}{9}+\dfrac{14}{9}\right)+\dfrac{1}{5}\)
\(=-\dfrac{3}{5}\cdot2+\dfrac{1}{5}\)
\(=-\dfrac{6}{5}+\dfrac{1}{5}\)
\(=-1\)

`a)[2x]/[-9]=10/91`

`=>2x.91=10.(-9)`

`=>182x=-90`

`=>x=-90/182`

`=>x=-45/91`

\(\Rightarrow2x\times91=10\times\left(-9\right)\\ \Rightarrow2x=\dfrac{-90}{91}\\ \Rightarrow x=\dfrac{-90}{91}:2\\ \Rightarrow x=-\dfrac{45}{91}\)

\(\dfrac{-1}{9}.\dfrac{3}{5}+\dfrac{-1}{4}.\dfrac{-4}{5}+\dfrac{1}{9}.\dfrac{2}{5}\)

\(\text{=}\dfrac{-1}{15}+\dfrac{1}{5}+\dfrac{2}{45}\)

\(\text{=}\dfrac{8}{45}\)

Áp dụng tính chất đổi dấu và giao hoán của phép nhân phân số, ta có:

\(\dfrac{-1}{9}.\dfrac{3}{5}+\dfrac{-1}{4}.\dfrac{-4}{5}+\dfrac{1}{9}.\dfrac{2}{5}=\dfrac{1}{5}.\dfrac{-3}{9}+\dfrac{1}{5}.\dfrac{4}{4}+\dfrac{1}{5}.\dfrac{2}{9}\)

                                           \(=\dfrac{1}{5}\left(-\dfrac{3}{9}+1+\dfrac{2}{9}\right)\)

                                           \(=\dfrac{1}{5}\left(-\dfrac{3}{9}+\dfrac{9}{9}+\dfrac{2}{9}\right)\)

                                           \(=\dfrac{1}{5}.\dfrac{8}{9}\)

                                           \(=\dfrac{8}{45}\)