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.
I think of it slightly differently, but it's basically the same:
In many germanic languages we say half-four when the time is half past three, where brits these days sometimes say half-three, to make it maximally confusing. I.e. we have an implied "half [to]" and they "half [past]".
This way of counting is what the Danes do. "Half-four times twenty" is "a half before four, times twenty" is "3.5 x 20" is 70 is "halvfjerdsindtyve" is "halvfjerds".
But it is only confusing to think of it that way, to speak Danish you have to just learn it as an opaque pointer to 70, or you'll get stuck doing mental arithmetic every time they say a number.
75 femoghalvfjerds used to be spoken as femoghalffjerdsindstyve, fem og half-fjerd-sinds-tyve¹, five and half-fourth-times-twenty.
The longer form is still used for ordinal numbers. 75th is femoghalffjerdsindstyvende.
French speakers will also recognise this system for numbers 80-99. 85 is quatre-vingt-cinq, four-twenties-five.
¹ People not used to compound words, like English speakers, will appreciate me writing it like this.