$a$) `1/2 . 25/3 : -2/15 . 12/24 - 1/3`
`= 1/2 . 25/3 . 15/-2 . 1/2 -1/3`
`= 1/4 . {125}/-2 - 1/3`
`= {125}/-8 - 1/3`
`= -383/24`
$b$) `5/8 + (-5/8 + -3/5) - 4/5 + 1`
`= 5/8 - 5/8 - 3/5 - 4/5 + 1`
`= -7/5 + 1`
`= -2/5`
$c$) `{2.(-13).9.10}/{-3.4.(-5).26}`
`= {-1.3.2}/{2.(-1).(-2)}`
`= {-6}/{4}`
`= {-3}/2`
$d$) `(1/3 + 12/67 + 13/41) - (79/67 - 28/41)`
`= 1/3 + 12/67 + 13/41 - 79/67 + 28/41`
`= -67/67 + 41/41 + 1/3`
`= -1 + 1 + 1/3`
`= 1/3`