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a, `14/15 + 4 5/17 + 1 1/15 - 3 5/17`

`= 14/15 + 73/17 + 16/15 - 56/17`

`= 14/15 + 73/17 + 16/15 + (-56)/17`

`= (14/15 + 16/15) + [73/17 + (-56)/17]`

`= 2 + 1`

`= 3`

b, `27 . (-1/3)^2 + 1/3 - 25 . (-1/5)^3 - 1/5`

`= 27 . 1/9 + 1/3 - 25 . (-1/125) - 1/5`

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

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

`= 9/3 + 1/3 + [1/5 + (-1)/5]`

`= 10/3 + 0`

`= 10/3`

c, `2/5 . 5/6 + 1/6 . (3/4 - 1/2)^2 . 6`

`= 1/3 + 1/6 . (1/4)^2 . 6`

`= 1/3 + 1/6 . 1/16 . 6`

`= 1/3 + 1/96 . 6`

`= 1/3 + 1/16`

`= 16/48 + 3/48`

`= 19/48`

d, `(5/2 - 1)^3 + (3/2 - 1/2)^2022`

`= (5/2 - 2/2)^3 + 1^2022`

`= (3/2)^3 + 1`

`= 27/8 + 1`

`= 27/8 + 8/8`

`= 35/8`