På fredag vil min søster købe flest grøntsager, fordi hun skal lave mad til begge børn.

På fredag literally means on Friday, but in everyday Danish it often means this coming Friday if the context is clear.

• på = on
• fredag = Friday

So På fredag is a very common way to place the action in time.

A learner might compare:

• på fredag = on Friday / this Friday
• om fredagen = on Fridays / every Friday in a habitual sense

Here, På fredag refers to one specific upcoming Friday.

This is because Danish is a V2 language in main clauses. That means the finite verb usually comes in the second position.

When the sentence begins with På fredag, that element takes the first position, so the verb vil must come second:

• På fredag = position 1
• vil = position 2
• min søster = then comes after the verb

So:

• Min søster vil købe flest grøntsager.
• På fredag vil min søster købe flest grøntsager.

Both are correct, but when you move På fredag to the front, the verb must stay second.

Here vil is being used to express the future, so it means something like will in English.

• vil købe = will buy

However, Danish vil can also sometimes mean want to, depending on context. In this sentence, the most natural reading is future:

• På fredag vil min søster købe ... = On Friday, my sister will buy ...

If you wanted a clearer idea of intention or plan, Danish can also use other expressions, but vil is very common for future meaning.

In Danish, plural count nouns are often used without an article when speaking generally or about an unspecified quantity.

So:

• købe grøntsager = buy vegetables

Just like in English, you would normally not say buy the vegetables unless you mean specific vegetables already known in the conversation.

Compare:

• hun køber grøntsager = she buys vegetables
• hun køber grøntsagerne = she buys the vegetables

Here, the vegetables are not specific, so grøntsager appears without an article.

Flest is the superlative form connected to quantity and means the most.

The forms are:

• mange = many
• flere = more
• flest = most

So:

• købe flest grøntsager = buy the most vegetables

This suggests comparison with others, even if the comparison is only implied.

By contrast:

• mere = more, usually used with uncountable nouns or in more general comparison
• flere = more, for countable plural nouns
• flest = most, for countable plural nouns

Since grøntsager is a plural countable noun, flest fits well.

No. Flest and de fleste are not used in exactly the same way.

• flest grøntsager = the most vegetables
• de fleste grøntsager = most vegetables / most of the vegetables, depending on context

In this sentence, flest is part of a comparison:

• min søster købe flest grøntsager = my sister will buy the most vegetables

That is why de is not used here.

Because fordi introduces a subordinate clause, and Danish word order changes in subordinate clauses.

In a main clause, Danish normally has V2 word order:

• Hun skal lave mad.

But after fordi, the clause is subordinate, and the word order becomes more like:

• fordi hun skal lave mad

So the structure is:

• fordi
  • subject
    • finite verb
      • rest

This is a very important pattern in Danish.

Compare:

• Main clause: Hun skal lave mad.
• Subordinate clause: ..., fordi hun skal lave mad.

They do different jobs:

• vil købe = will buy
• skal lave mad = has to cook / is going to cook

Here:

• vil expresses what will happen in the future
• skal expresses necessity, obligation, or a planned task

So the logic is:

• My sister will buy the most vegetables
• because she has to cook for both children

In many contexts, skal can sound like has to, must, or is supposed to.

Lave mad is the standard Danish expression for cook / make food.

• lave = make
• mad = food

Together, lave mad means to cook.

This is just an idiomatic expression you should learn as a chunk.

Examples:

• Jeg laver mad. = I am cooking.
• Hun skal lave mad. = She has to cook.

Danish does also have koge and stege, but those are more specific:

• koge = boil
• stege = fry/roast

So lave mad is the broad everyday expression.

In this sentence, til is the natural preposition because it means the food is being prepared for them in the sense of intended for / served to them.

• lave mad til nogen = cook food for someone

So:

• hun skal lave mad til begge børn = she has to cook for both children

English uses for, but Danish commonly uses til in this expression.

Begge already works as a determiner here, so begge børn means both children.

• begge børn = both children

You can also hear begge børnene, but that is more explicitly definite: both of the children / both the children.

In many contexts, begge børn is perfectly natural and enough on its own.

So the difference is roughly:

• begge børn = both children
• begge børnene = both the children / both of the children

Yes. Standard Danish spelling uses a comma before a subordinate clause, and fordi introduces one here.

So:

• På fredag vil min søster købe flest grøntsager, fordi hun skal lave mad til begge børn.

That comma is normal and expected in written Danish.

It would be:

• Min søster vil købe flest grøntsager på fredag, fordi hun skal lave mad til begge børn.

This is also correct.

The difference is mainly focus:

• På fredag ... puts the time first for emphasis
• Min søster ... puts the subject first in a more neutral way

Both are natural Danish, but the original sentence highlights when this will happen.