Er hat sich weniger vorgenommen als sie
Why does this sentance translate to : "He has decided to do less than them" and not to "He has made/done less than them?"
'sich etwas vornehmen' means 'to resolve to do sth.' It's a shorter version of 'Sich vornehmen etwas zu tun' . 'He has made/done less than them' would be 'Er hat weniger gemacht/getan als sie'. Be careful: 'sich jemanden vornehmen' has a totally different meaning that depends strongly on the context and - as far as I know - has no real equivalent in English. In a first order approximation 'ich werde ihn mir vornehmen' means something like 'I'll deal with him in a hard/strict manner'
The sentence means: The amount of work he has decided to do is less than the amount they have decided to do. 'sich etwas vornehmen' = 'to decide to do sth.' 'sich weniger vornehmen' = 'to decide to do sth. that has a lesser amount' ~ 'to decide to do less' (Note that there is a slight shift in meaning here. The exact meaning of the German sentence is close to the left-hand side of the ~). 'Er hat sich weniger vorgenommen als sie' = 'He has decided to do less than they have'. The translation 'he has decided to do less than them' isn't exactly on the mark. That would rather be 'Er hat sich vorgenommen, weniger zu tun als sie'. (The difference in meaning is: In the 'er hat sich weniger vorgenommen als sie' case, he and the group both have independently decided to do a certain amount of sth. and by chance his amount is less while in the other case it is his goal to do less than them.)