Difference between halva och hälften in Swedish language

The Swedish language is much more complicated than English due to words that exist in English only as one word, while Swedish has two and sometimes many more words for that word. These words are translated as same into English, but they are not interchangeable in Swedish. In other words, you have to understand their differences and use them properly.

So, what is the difference between halva och hälften in Swedish, since both mean “half” in English? 
First of all, these words are used differently, even if you want to express the same thing. We can examine these words’ differences when they stay next to other nouns since when we speak of half of something, we must mention half of what. Let’s take a fish as an example:

“Half of the fish”

In that case, both hälften and halva are correct to use in the Swedish language, but these words are used differently. In the case of the fish, it is:
“halva fisken” and if you want to use “hälften” then you have to use the preposition “av” which corresponds to English “of”. In that case it is “hälften av fisken” . Both “halva fisken” and “hälften av fisken” mean same thing and in that case it is interchangible in Swedish.

For example, My cat ate half of the fish.
In Swedish: Min katt åt halva fisken or Min katt åt hälften av fisken. The meaning is same and thats why halva and hälften av here is interchangible.

Yet, we have cases where one can not replace them with one another.
When we speak about a part of a quantity in Swedish, you will use the word “hälften” while for more concrete half of something we use “halva”. 

Lets continue with the fish as an example and assume that you have bought 10 herrings, so to say 10 fishes, which means we deal with a quantity. So, out of these ten herrings, that quantity, five fishes are rotten, in other words “Half of the fish are rotten“
“Hälften av fiskarna är ruttna“. In this case we speak about quanity of fishes that are rutton.
If we speak about half of one concrete fish, we have to use “halva”.

Let’s assume that I cut one fish into two parts in disproportional halves, and my cat is lucky to get the bigger part or a bigger half of it. “My cat got the big half of the fish.”,“Min katt fick den stora halvan av fisken”

It is also important to understand that “halva” and “hälft” are nouns, substantiv.

“halva” as a noun is a singular indefinite form, and “halvan” is a singular definite equally “halvor” is plural indefinite and “halvorna” is a plural definite. You should not confuse it with “halv” as adjektive, because “ett-form” of that is”halvt” and the plural is “halva”! As mentioned, “hälft” is also a noun, singular indefinite. The singular definite form is “hälften“, plural indefinite is “hälfter“, and plural definite is “hälfterna“. But most often, the noun “hälft” is used as singular definite, “hälften“