Hjálpartækið er niðurgreitt.

Because Icelandic, like the other Germanic languages, makes compound nouns very freely. Hjálpartæki is a compound noun meaning something like assistive device or aid device.

It is built from:

• hjálp = help, assistance
• tæki = device, tool, apparatus

In compounds, the first part often changes form slightly, so you get hjálpar- + tæki rather than a simple hjálp + tæki.

So hjálpartæki is a normal Icelandic-style compound noun.

Icelandic usually puts the definite article onto the end of the noun instead of using a separate word.

So:

• hjálpartæki = an assistive device / assistive device
• hjálpartækið = the assistive device

The ending -ið here is the neuter singular definite article.

It is neuter.

That matters because adjectives and participles must agree with the noun in gender, number, and case. Since hjálpartækið is neuter singular, the describing word after er also appears in a neuter singular form: niðurgreitt.

Because niðurgreitt agrees with the neuter singular subject hjálpartækið.

The participle/adjective has different forms:

• masculine singular: niðurgreiddur
• feminine singular: niðurgreidd
• neuter singular: niðurgreitt

So:

• Bíllinn er niðurgreiddur = the car is subsidized
• Þjónustan er niðurgreidd = the service is subsidized
• Hjálpartækið er niðurgreitt = the assistive device is subsidized

It is basically a past participle used like an adjective.

The verb is niðurgreiða, meaning to subsidize. Its past participle is:

• niðurgreiddur / niðurgreidd / niðurgreitt

After er, Icelandic often uses a participle this way, much like English does in sentences such as is subsidized.

So in this sentence, niðurgreitt functions as a predicate complement after er.

Er is the present tense, 3rd person singular form of vera, which means to be.

So:

• ég er = I am
• þú ert = you are
• hann / hún / það er = he / she / it is

Since hjálpartækið is singular, the sentence uses er.

It is in the nominative case, because it is the subject of the sentence.

The sentence structure is:

• Hjálpartækið = subject
• er = verb
• niðurgreitt = predicate complement

One slightly tricky point is that for many neuter nouns, nominative and accusative look the same. So the form hjálpartækið could also be accusative in another sentence, but here it is nominative because it is the subject.

No, this is a very straightforward Icelandic sentence.

It follows the basic pattern:

• subject + verb + complement

So:

• Hjálpartækið = subject
• er = verb
• niðurgreitt = complement

This is very similar to English The assistive device is subsidized.

That said, Icelandic is a verb-second language, so in other sentence types the verb still tends to stay in second position:

• Í dag er hjálpartækið niðurgreitt = Today the assistive device is subsidized

A rough learner-friendly pronunciation might be:

HYAL-par-tye-kith er NITH-ur-grayht

A few useful points:

• hj at the start of hjálp- is not pronounced like normal English h
  • y; it is a softer Icelandic sound.
• æ is like the vowel in eye.
• ð in niður- is like the th in this.
• ei in greitt sounds like ay in say.
• tt in Icelandic is often pronounced differently from English tt and may sound preaspirated to learners.

If you want to sound natural, listening to native audio is especially helpful for words like hjálpartækið and niðurgreitt, because their consonants are more complex than English spelling suggests.

It would be:

Hjálpartæki er niðurgreitt.

But that sentence is less natural in many contexts, because singular count nouns are often definite or otherwise specified in actual use.

The important contrast is:

• hjálpartæki = assistive device / an assistive device
• hjálpartækið = the assistive device

So the -ið is the key difference.

Historically and structurally, yes, it is connected to the idea of payment, since the verb greiða relates to paying, and niður- adds the sense of reduction or downward movement.

But as a learner, the safest thing is to understand niðurgreiða as a fixed verb meaning to subsidize, and niðurgreitt as subsidized.

So although the literal pieces can help you remember it, the real meaning in modern usage is the important part.