`a) ( - 2 )/3 + 3/4 + ( - 5 )/6`

`= ( - 8 )/12 + 9/12 + ( - 10 )/12`

`= 1/12 + ( - 10 )/12`

`= ( - 9 )/12 = ( - 3 )/4`

`b) 1/6 + 7/3 - 1/2`

`= 1/6 + 14/6 - 3/6`

`= 15/6 - 3/6`

`= 12/6 = 2`

`c) 4/3 - ( 12/9 - 2022 )`

`= 4/3 - 12/9 + 2022`

`= 4/3 - 4/3 + 2022`

`= 0 + 2022`

`= 2022`

`d) 3/4  + ( 2019 - 21/28 )`

`= 3/4 + 2019 - 21/28`

`= ( 3/4 - 21/28 ) + 2019`

`= ( 3/4 - 3/4 ) + 2019`

`= 0 + 2019`

`= 2019`

`e) ( ( - 1 )/4 + 5/8 ) - 3/8`

`= ( - 1 )/4 + 5/8 - 3/8`

`= ( - 1 )/4 + ( 5/8 - 3/8 )`

`= ( - 1 )/4 + 1/4`

`= 0`

`f) 8 2/7 - ( 3 4/9 + 4 2/7 )`

`= 8 2/7 - 3 4/9 - 4 2/7`

`= ( 8 2/7 - 4 2/7 ) - 3 4/9`

`= 4 - 31/9`

`= 36/9 - 31/9`

`= 5/9`

 a) $\frac{-2}{3}$+$\frac{3}{4}$+$\frac{-5}{6}$

   =$\frac{-8}{12}$+$\frac{9}{12}$+$\frac{-15}{12}$

   =$\frac{-14}{12}$=$\frac{7}{6}$

b) $\frac{1}{6}$+$\frac{7}{3}$-$\frac{1}{2}$

   =$\frac{1}{6}$+$\frac{14}{6}$-$\frac{3}{6}$

   =$\frac{12}{6}$=2

c)$\frac{4}{3}$-($\frac{12}{9}$-2022)

   =$\frac{4}{3}$-$\frac{12}{9}$+2022

   =$\frac{12}{9}$-$\frac{12}{9}$+2022

   =0+2022=2022

d) $\frac{3}{4}$+(2019-$\frac{21}{28}$)

   =$\frac{3}{4}$+2019-$\frac{21}{28}$

   =($\frac{3}{4}$-$\frac{21}{28}$)+2019

   =($\frac{21}{28}$-$\frac{21}{28}$)+2019

   =0+2019=2019

e) ($\frac{-1}{4}$+$\frac{5}{8}$)+$\frac{-3}{8}$

   =$\frac{-1}{4}$+($\frac{5}{8}$+$\frac{-3}{8}$)

   =$\frac{-1}{4}$+$\frac{1}{4}$

   =0

f) 8$\frac{2}{7}$-(3$\frac{4}{9}$+4$\frac{2}{7}$)

   =8$\frac{2}{7}$-3$\frac{4}{9}$-4$\frac{2}{7}$

   =(8$\frac{2}{7}$-4$\frac{2}{7}$)-3$\frac{4}{9}$

   =4-$\frac{31}{9}$

   =$\frac{36}{9}$-$\frac{31}{9}$

   =$\frac{5}{9}$