Til frokost spiser de en skive rugbrød med ost og lidt syltetøj.

Both are possible, but they do slightly different things.

Danish main clauses normally follow the verb-second (V2) rule. That means the finite verb must come in the second position.

• De spiser til frokost ... = the subject de comes first
• Til frokost spiser de ... = the time phrase til frokost comes first, so the verb spiser must come next, before de

So when Til frokost is moved to the front for emphasis or topic, Danish word order becomes:

• Til frokost = first element
• spiser = second element
• de = subject after the verb

This is very common in Danish.

Literally, til frokost means something like for lunch or at lunch.

In Danish, til is often used in fixed time expressions connected with meals:

• til morgenmad = for breakfast / at breakfast
• til frokost = for lunch / at lunch
• til aftensmad = for dinner

So this is a natural idiomatic expression, even if it does not match English word-for-word.

Spiser is the present tense of at spise = to eat.

The forms are:

• at spise = to eat
• spiser = eat / eats / are eating / is eating, depending on context
• spiste = ate
• har spist = have eaten / has eaten

Danish present tense is often simple: you usually add -r to the infinitive.

Also, Danish present tense can cover both English simple present and present continuous, depending on context.

So de spiser can mean:

• they eat
• they are eating

In modern everyday Danish, de here means they.

Historically and in more formal language, De with a capital D could be a formal you, but that is old-fashioned and uncommon in normal modern conversation.

So in this sentence, learners should understand de simply as they.

Because skive is a common gender noun, so it takes en.

• en skive = a slice

The article agrees with skive, not with rugbrød.

That is important because the phrase means:

• en skive rugbrød = a slice of rye bread

The main noun in the phrase is skive, and rugbrød just tells you what kind of slice it is.

English uses of here, but Danish often leaves it out in this kind of expression.

So Danish commonly says:

• en skive rugbrød = a slice of rye bread
• et glas vand = a glass of water
• en kop kaffe = a cup of coffee

You may sometimes see af in other contexts, but in everyday Danish these measure/container expressions often appear without it.

Because rugbrød is being used like a material or substance noun here, not as a separate counted object.

The phrase is not really:

• a slice + a rye bread

It is:

• a slice of rye bread

So rugbrød works more like an uncountable substance in this expression.

Compare:

• en skive rugbrød = a slice of rye bread
• et rugbrød = a rye loaf / a rye bread

Both are possible, but they are different structures.

Because ost here means cheese as a mass noun, not a cheese as a whole item or type.

In English, you also normally say:

• with cheese

not:

• with a cheese

So in Danish:

• med ost = with cheese

If you said en ost, that would usually mean a cheese as a whole cheese or a specific cheese item.

Lidt means a little or some.

So:

• lidt syltetøj = a little jam / some jam

It is very common with uncountable nouns:

• lidt vand = a little water
• lidt kaffe = a little coffee
• lidt sukker = a little sugar

Here it makes the phrase sound natural and specific: not a large amount, just a bit of jam.

Because syltetøj is also being used as an uncountable noun here, like jam in English.

So:

• lidt syltetøj = a little jam / some jam

You would not normally say et syltetøj in this meaning.

Yes. It describes what is on or with the slice of rye bread.

So the structure is:

• en skive rugbrød = a slice of rye bread
• med ost og lidt syltetøj = with cheese and a little jam

Together:

• en skive rugbrød med ost og lidt syltetøj

In natural English, that would usually mean a slice of rye bread with cheese and a little jam on it.

Yes, it is a very common and culturally important Danish word.

Rug = rye
Brød = bread

So rugbrød literally means rye bread, but in Denmark it often refers to the dark, dense bread that is a standard part of everyday meals, especially lunch.

That is why this sentence sounds very natural and typical in a Danish context.

Yes, absolutely.

That version is also correct:

• De spiser en skive rugbrød med ost og lidt syltetøj til frokost.

The difference is mostly about emphasis and information flow:

• Til frokost spiser de ... puts the focus on when
• De spiser ... til frokost starts with who

Both are natural Danish sentences.

Usually yes, but you should know that meal terms do not always match perfectly across cultures.

In standard Danish:

• morgenmad = breakfast
• frokost = lunch
• aftensmad = dinner/evening meal

So in this sentence, frokost is clearly lunch. However, what people actually eat for frokost in Denmark may be different from what English speakers imagine as lunch.

You could say:

• Til frokost spiser han en skive rugbrød med ost og lidt syltetøj.
• Til frokost spiser hun en skive rugbrød med ost og lidt syltetøj.

Only the subject changes:

• de = they
• han = he
• hun = she

The verb spiser stays the same, because Danish verbs do not change for person the way English verbs sometimes do.