Sorry, I should have explained that better.
It's half of the fourth twenty — meaning all of the first, second and third twenties, but only half of the fourth one. 20 + 20 + 20 + ½×20 = 70.
And for the 75, it's just "five and" before all that.
Many native Danish speakers learn the abbreviated words as young children, and don't generally think about their numbers this way, if they're even aware of it. (Much as a native English speaker might not think of 'thirteen' as 'three-ten'.)
For 60 and 80, the normal, abbreviated form is very short: "tres" and "firs" (full form: "tresindstyve", "firsindstyve"). For foreigners, these sound rather like something to do with three and four — as they are! — which causes much more difficulty than expected when learning basic numbers.
("Much more difficulty than expected" is the general experience when learning Danish as a second language: https://www.youtube.com/watch?v=eI5DPt3Ge_s)