Translation:The farmer will try to increase the amount of fruit.
Only in this lesson we have these examples:
"Biblioteket vil øge antallet af bøger." : "The library wants to increase the number of books."
"Landmanden vil prøve at øge mængden af frugt." : "The farmer will try to increase the amount of fruit."
I fail to see the reason for the different translations.
I think technically it would be "the number of fruits" ("antallet af frugter" though this could also be the quantity of an unspecified fruit in Danish, I believe, whereas here it's not necessarily whole fruits) but I know that a lot of people, at least in English, do use "amount" with a countable noun
So both in English and Danish "fruit"/frugt can take singular form when talking about uncountable quantity and mængde enforces it here. Correct?
Actually I dug into my Latvian brain and realized that we have the same concept fx for siers (cheese) and gaļa (meat), but it doesn't apply to auglis (fruit). And we use daudzums (amount) very loosely both for uncountable and countable things.
To expand on btwillbethere's idea and Xneb's clarification:
In Latvian one can say siera [sg.] daudzums (amount of cheese) and sieru [pl.] daudzums (number [variety] of cheeses).
As evidenced, in English (at least American) also one could say "the amount of cheeses" and mean number of various kinds of cheese.
In Danish, apparently, mængde can only be used with uncountable things. And it forces the uncountable nature for dual things.