Það er bannað að hlaupa á sleipum stigum í skólunum.

It is forbidden to run on slippery stairs in the schools.

Breakdown of Það er bannað að hlaupa á sleipum stigum í skólunum.

• vera: to be
• það: it
• skólinn: the school
• á: on
• í: in
• hlaupa: to run
• sleipur: slippery
• bannaður: forbidden
• stiginn: the stair

Questions & Answers about Það er bannað að hlaupa á sleipum stigum í skólunum.

Why does the sentence start with Það er? Is það really "it" here?

Here það is a dummy / expletive subject, not a real thing. It works just like English It in:

• It is forbidden to run on slippery stairs.
• It is raining.

Icelandic often uses Það er + adjective/participle + að + infinitive to talk generally about what is allowed, possible, hard, forbidden, etc.

So:

• Það er bannað að hlaupa…
  = It is forbidden to run… (general statement, not about any specific “it”)

Why is it bannað and not something like bannaður or bönnuð?

Bannað is the neuter singular form of the past participle of að banna (to forbid).

In impersonal sentences like this, Icelandic normally uses the neuter singular as a kind of default form, because there is no real, concrete subject:

• Það er bannað að hlaupa… – It is forbidden to run…
• Það er leyfilegt að… – It is allowed to…
• Það er erfitt að… – It is hard to…

Forms like bannaður / bönnuð / bannað (masc/fem/neut) would be used only when the participle is agreeing with some actual noun:

• Strákurinn er bannaður inn í herbergið. – The boy is banned from the room. (masc)
• Konan er bönnuð hér. – The woman is banned here. (fem)

Here there is no such noun, so the neutral bannað is used.

What exactly is að hlaupa grammatically? Why do we need að here?

Að hlaupa is the infinitive form: to run.

• hlaupa = base verb to run
• að = infinitive marker to

In Icelandic, when you use a verb after adjectives or participles like bannað, leyfilegt, erfitt, you normally use að + infinitive:

• Það er bannað að hlaupa. – It is forbidden to run.
• Það er gott að læra íslensku. – It is good to learn Icelandic.

You cannot drop að in this structure.
*Það er bannað hlaupa is ungrammatical. (You only drop að after some modal verbs like má, þarf, á.)

Why is it á sleipum stigum and not something like á sleipa stiga?

The preposition á can take either accusative or dative, depending on meaning:

• Accusative: motion onto / into something
• Dative: location on/in something (no movement to a new place)

In your sentence, we are talking about being / running on stairs (location), not moving onto them:

• á sleipum stigum – on slippery stairs (location → dative plural)

So:

• stigum is dative plural of stig (a neuter noun)
• sleipum is the dative plural form of the adjective sleipur, agreeing with stigum

If you expressed motion onto the stairs, you would use accusative plural:

• Hann hljóp á sleip stig. – He ran onto slippery stairs. (accusative plural; different meaning)

What does sleipum mean exactly, and why that ending?

Sleipum is the dative plural form of the adjective sleipur, which means roughly slippery / slick / greasy.

The base forms of the adjective:

• Nominative singular:
  
  • masc: sleipur
  • fem: sleip
  • neut: sleipt

In á sleipum stigum:

• stigum is dative plural, so the adjective must also be dative plural: sleipum
• All genders share -um in dative plural for strong adjectives.

So the phrase is:

• á sleipum stigum = on slippery stairs (both words in dative plural)

What is stigum? Does stig mean "step" or "stairs" or something else?

Stig is a neuter noun with several meanings, including:

• step, stair (individual step or the staircase, depending on context)
• degree, level, stage (e.g. in abstract uses)

In this sentence, stigum is the dative plural of stig, so:

• stigin – the step / the stair (nom. sing. with article)
• stigum – steps / stairs (dat. pl.)

Here, á sleipum stigum naturally means on slippery stairs / on slippery steps.
Icelandic often uses stig and stigi (another noun) in stair-related contexts:

• stig – step/steps, stair(s)
• stigi – stairway, ladder

Why is it í skólunum and not í skólanum or just í skóla?

Breakdown:

• skóli – a school (nominative singular)
• skólum – dative plural
• skólunum – dative plural with the definite article (the schools)

The preposition í with location usually takes dative:

• í skóla – in a school (dat. sing., indefinite)
• í skólanum – in the school (dat. sing., definite)
• í skólum – in schools (dat. pl., indefinite)
• í skólunum – in the schools (dat. pl., definite)

Í skólunum is literally in the schools, which often has a general meaning like in schools (as an institution) in this kind of rule sentence. English often prefers the singular at school / in school, but Icelandic can use the plural skólunum to talk about all the relevant schools collectively.

Could the word order be Það er bannað að hlaupa í skólunum á sleipum stigum? Would that change the meaning?

Yes, you can say:

• Það er bannað að hlaupa í skólunum á sleipum stigum.

This is still correct and means essentially the same thing.
Both orders are possible:

1. … að hlaupa á sleipum stigum í skólunum.
2. … að hlaupa í skólunum á sleipum stigum.

Nuance:

• Order (1) groups á sleipum stigum more tightly with hlaupa: to run on slippery stairs (where? in the schools).
• Order (2) might sound a bit more like to run in the schools (where? on slippery stairs).

In practice, the difference is very small here; both would normally be understood the same.

Is there another common way to express the same idea in Icelandic, maybe closer to English "you must not run"?

A very natural alternative is to use má ekki (must not / may not):

• Má ekki hlaupa á sleipum stigum í skólunum.
• Það má ekki hlaupa á sleipum stigum í skólunum.

These are very typical for rules, signs, and spoken instructions, roughly:

• You must not run on slippery stairs in schools.
• One may not run on slippery stairs in schools.

Your original sentence with Það er bannað að… is also perfectly normal, slightly more explicit about forbidden.

What would be a more natural English translation? Do we really say "in the schools"?

The literal translation is:

• It is forbidden to run on slippery stairs in the schools.

But idiomatic English would usually say something like:

• Running on slippery stairs at school is forbidden.
• You must not run on slippery stairs at school.
• No running on slippery stairs at school.

English tends to use at school / in school rather than in the schools when expressing general rules, while Icelandic í skólunum comfortably covers that general meaning.