I dag lærer vi at bruge mere og mindre med ting, man ikke kan tælle, og flere og færre med ting, man kan tælle.

Yes, you could also say Vi lærer i dag .... Both are correct, but the emphasis is different.

• I dag lærer vi ... puts focus on today
• Vi lærer i dag ... puts focus more on we learn

This is also a good example of the Danish V2 rule: in a main clause, the finite verb usually comes in the second position.

So when I dag comes first, the verb lærer must come before vi:

• I dag lærer vi ...
• not I dag vi lærer ...

At bruge means to use.

In Danish, at is the infinitive marker, like English to before a verb in its basic form.

So:

• bruge = use
• at bruge = to use

In this sentence, lærer vi at bruge means we are learning to use.

This is one of the main grammar points in the sentence.

Danish distinguishes between:

• uncountable things → mere and mindre
• countable things → flere and færre

So:

• mere vand = more water
• mindre sukker = less sugar
• flere æbler = more apples
• færre bøger = fewer books

This is similar to formal English:

• more / less for uncountable nouns
• more / fewer for countable nouns

A native English speaker may notice that English uses more for both countable and uncountable nouns, but Danish does not. Danish uses:

• mere with uncountable
• flere with countable

Ting means things.

In this sentence, it is being used in a general way to talk about all kinds of nouns or items:

• ting, man ikke kan tælle = things that cannot be counted
• ting, man kan tælle = things that can be counted

It is a broad, everyday word. The sentence is explaining a rule, so ting works as a general category instead of listing specific examples.

Here, man means something like:

• one
• you in a general sense
• people

So ting, man ikke kan tælle literally means things that one cannot count, but in natural English we would usually say things you cannot count or things that cannot be counted.

This man is very common in Danish when speaking generally.

Examples:

• Man siger ... = People say ... / You say ...
• Man kan ikke vide det = You cannot know that / One cannot know that

Because this part is a subordinate clause.

In Danish subordinate clauses, words like ikke usually come before the finite verb.

So:

• main clause: Man kan ikke tælle det
• subordinate clause: ting, man ikke kan tælle

This is a very important word-order pattern in Danish.

Compare:

• Jeg ved, at han ikke kommer = I know that he is not coming
• Hun siger, at de ikke forstår det = She says that they do not understand it

So the position of ikke helps show that this is not a main clause.

Literally, kan tælle means can count.

In this sentence, it really means can be counted or are countable.

So:

• ting, man kan tælle = things you can count individually
• ting, man ikke kan tælle = things you do not normally count individually

For example:

• æbler are countable → flere æbler
• vand is uncountable → mere vand

Danish often expresses this idea with kan tælle, even where English learners might think in terms of countable and uncountable.

Med means with here.

The structure is:

• bruge mere og mindre med ...
• og flere og færre med ...

So the sentence means:

• use mere and mindre with uncountable things
• and flere and færre with countable things

Repeating med makes the sentence clearer and neatly separates the two rules.

You might compare it to English:

• we use more and less with uncountable nouns, and more and fewer with countable nouns

Yes, they are all comparative words.

They correspond roughly to:

• mere = more
• mindre = less
• flere = more, but for countable nouns
• færre = fewer

They are related to these basic quantity words:

• meget → mere
• mange → flere
• få → færre

Mindre is used as less in quantity.

So this sentence is really about choosing the correct comparative quantity word depending on whether the noun is countable or uncountable.

Those commas separate off clauses that describe ting.

So:

• ting, man ikke kan tælle
• ting, man kan tælle

These are relative-type descriptions: things that you cannot count and things that you can count.

Danish punctuation often uses commas to mark subordinate clauses more clearly than English does. So for an English speaker, the commas may look a little heavier or more frequent than expected.

Yes:

With uncountable nouns:

• mere vand = more water
• mindre kaffe = less coffee
• mere tid = more time
• mindre sukker = less sugar

With countable nouns:

• flere bøger = more books
• færre biler = fewer cars
• flere æbler = more apples
• færre stole = fewer chairs

A good shortcut is:

• if you can count them one by one, use flere or færre
• if you normally do not count them one by one, use mere or mindre