Jeg tager den forkerte bog med til biblioteket.

In Danish, when a noun is definite and has an adjective before it, the usual pattern is:

den/det/de + adjective + noun

So:

• den forkerte bog = the wrong book

Here:

• den marks definiteness
• forkerte is the adjective
• bog stays in its basic singular form

If there were no adjective, you would normally say:

• bogen = the book

So:

• bogen = the book
• den forkerte bog = the wrong book

Danish does not normally say den forkerte bogen.

Because bog is a common gender noun, not a neuter noun.

In Danish, singular nouns are either:

• en-words (common gender)
• et-words (neuter)

You learn bog as:

• en bog = a book

So in a definite phrase with an adjective, it becomes:

• den forkerte bog

If the noun were a neuter et-word, you would use det instead.

Because adjectives in Danish change form depending on grammar.

The basic form is:

• forkert

But in a definite noun phrase like den ... bog, the adjective usually takes -e:

• den forkerte bog

So this is the normal definite/weak adjective form.

Compare:

• en forkert bog = an incorrect/wrong book
• den forkerte bog = the wrong book

That -e ending is very common after den, det, and de when an adjective comes before the noun.

Because tage med is a very common Danish verb combination meaning take along / bring.

Its dictionary form is:

• at tage med

But in an actual sentence, the particle med is often separated from the main verb:

• Jeg tager den forkerte bog med

So you can think of it as:

• tager ... med = take ... along

This is similar to English phrasal verbs like pick ... up or take ... along, where one part of the verb can appear later in the sentence.

It means something like take along, bring, or take with you, depending on context.

So:

• Jeg tager bogen med = I’m taking the book with me / I’m bringing the book

Danish often uses tage med where English might choose either take or bring. The exact English choice depends on point of view, but the Danish structure itself is very normal.

Because til expresses movement toward a destination:

• til biblioteket = to the library

If you said i biblioteket, that would mean in the library, which describes location rather than direction.

So compare:

• Jeg går til biblioteket = I go to the library
• Jeg er i biblioteket = I am in the library

In your sentence, the book is being taken to the library, so til is the right preposition.

Because bibliotek is a neuter noun:

• et bibliotek = a library

Its definite singular form is made with -et:

• biblioteket = the library

So:

• et bibliotek = a library
• biblioteket = the library

That is the normal definite ending for many singular neuter nouns.

Yes. Danish present tense often covers both:

• things happening now
• habits
• planned or expected future actions

So Jeg tager den forkerte bog med til biblioteket can mean something like:

• I am taking the wrong book to the library
• I take the wrong book to the library
• I’m going to take the wrong book to the library

The exact time meaning depends on context. This is very natural in Danish and is similar to how English can sometimes use the present for future arrangements.

The sentence follows a very normal Danish main-clause order:

Subject + verb + object + particle + prepositional phrase

So here:

• Jeg = subject
• tager = verb
• den forkerte bog = object
• med = particle
• til biblioteket = prepositional phrase

That gives:

• Jeg tager den forkerte bog med til biblioteket.

This is a straightforward declarative sentence pattern in Danish.