Må jeg låne din blyant?

Because må is a modal verb (may / be allowed to / can in the sense of permission). In Danish main clauses, when you form a question, the finite verb usually comes first (V2 rule), so you get:

• Statement: Jeg må låne din blyant.
• Question: Må jeg låne din blyant?

Må is about permission or acceptability: May I…?/Am I allowed to…?
Kan is about ability or possibility: Can I…?/Am I able to…?

In everyday Danish, people often use kan for polite requests too, but the nuance is:

• Må jeg låne din blyant? = asking permission (very natural here)
• Kan jeg låne din blyant? = asking if it’s possible / okay (also very common)

After a modal verb like må, Danish uses the bare infinitive (without at):

• Jeg må låne… (I may borrow…) Not:
• Jeg må låner… (incorrect)

So må + infinitive is the pattern.

No. After modal verbs (må, kan, vil, skal, bør), you typically don’t use at:

• Må jeg låne… (correct)
• Må jeg at låne… (incorrect)

You would use at in other infinitive constructions, e.g. Jeg prøver at låne en blyant.

It depends on the gender/number of the noun:

• din = common gender singular (en-words)
• dit = neuter singular (et-words)
• dine = plural

Blyant is common gender: en blyant, so it takes din: din blyant.

Because you already specify whose pencil it is with din. In Danish, a possessive usually replaces the indefinite article:

• en blyant = a pencil
• din blyant = your pencil (not en din blyant)

In this sentence, din is singular “your” (talking to one person). Danish distinguishes:

• din/dit/dine = your (one person, informal)
• jeres = your (plural “you”)
• Deres = your (formal/polite “you” in writing or very formal speech)

So din here assumes you’re speaking to one person informally.

A rough guide:

• må: like English moh with a long vowel (Danish å is a long open “aw/oh”-type sound depending on accent).
• jeg: often sounds like yai or a softened yei in many accents (the g is not a hard “g”).
• låne: LOH-neh (first syllable stressed)
• blyant: roughly BLÜ-an(t) (the y is a front rounded vowel, not English “y”)

Exact pronunciation varies by region, but the key surprises for English speakers are å, the soft jeg, and Danish y.

Yes, it’s polite and normal. Variants:

• Neutral/polite: Må jeg låne din blyant?
• Very common everyday request: Kan jeg låne din blyant?
• More polite/softened: Må jeg lige låne din blyant? (adds lige = “just/for a moment”)
• More direct: Jeg vil gerne låne din blyant. (“I’d like to borrow your pencil.”)

Very formal address would typically involve Deres (rare in speech): Må jeg låne Deres blyant?

In Danish:

• låne = to borrow (take and use temporarily)
• låne … ud = to lend out

So Må jeg låne din blyant? clearly means May I borrow your pencil?
If you mean “Can you lend me your pencil?”, you’d typically say:

• Kan du låne mig din blyant? (common) or more explicitly:
• Kan du låne din blyant ud til mig?

The basic structure here is fixed: Må (verb) + jeg (subject) + låne (infinitive) + din blyant (object)

You can add adverbs, but they usually go after the subject:

• Må jeg lige låne din blyant?
• Må jeg hurtigt låne din blyant?

Keeping the verb-first question order is the main thing.