Den nye metode er mere effektiv end den gamle.

Den means the for a common-gender singular noun. The noun metode is a common-gender word, so its definite form uses den.

In this sentence, Den nye metode means the new method.

A useful pattern is:

• den + adjective + noun for common-gender singular
• det + adjective + noun for neuter singular
• de + adjective + noun for plural

So because metode is common gender, Danish uses den.

When an adjective comes before a noun in a definite phrase like the new method, Danish usually uses the -e form of the adjective.

So:

• en ny metode = a new method
• den nye metode = the new method

That is why you get nye, not ny.

Danish forms comparatives in two main ways:

1. with an ending, like stærk → stærkere
2. with mere + adjective, like mere effektiv

With many longer adjectives, especially ones that feel more formal or are borrowed from other languages, Danish often prefers mere.

So:

• mere effektiv = more effective

For a learner, mere + adjective is a very safe pattern with longer adjectives.

End means than in comparisons.

So the pattern is:

• mere X end Y = more X than Y

In your sentence:

• mere effektiv end den gamle = more effective than the old one / than the old method

Be careful not to confuse end with og.

• end = than
• og = and

Because Danish, like English, often leaves out a noun when it is already understood.

So:

• den gamle literally means the old
• but here it really means the old one or the old method

The full version would be:

• Den nye metode er mere effektiv end den gamle metode.

But repeating metode is unnecessary, so Danish naturally shortens it to den gamle.

For the same reason as nye: it is in a definite phrase.

Compare:

• en gammel metode = an old method
• den gamle metode = the old method

When the noun is understood and left out, the adjective still stays in that definite -e form:

• den gamle = the old one

The structure is:

• Den nye metode = subject
• er = verb
• mere effektiv = complement
• end den gamle = comparison phrase

So the full pattern is:

subject + verb + comparative + end + comparison

This is very similar to English:

The new method + is + more effective + than + the old one.

No. If you are comparing two things, Danish needs a comparative form.

So you need either:

• mere effektiv = more effective
• or, with other adjectives, a form in -ere

That means:

• Den nye metode er mere effektiv end den gamle. ✅
• Den nye metode er effektiv end den gamle. ❌

Without mere, the sentence only says effective, not more effective.

That would mean something different.

• mere effektiv = more effective
  compares two things
• den mest effektive = the most effective
  means it is at the top of a larger group

So:

• Den nye metode er mere effektiv end den gamle.
  = the new method is more effective than the old one

• Den nye metode er den mest effektive.
  = the new method is the most effective

Both are correct, but they do not mean the same thing.

Danish main clauses usually follow the V2 rule, which means the finite verb comes in the second position.

Here the first element is:

• Den nye metode

So the verb comes next:

• er

That gives:

• Den nye metode er mere effektiv end den gamle.

This word order is one of the most important patterns in Danish.

If the noun were neuter, you would use det instead of den.

For example:

• det nye system = the new system

So the pattern would become:

• Det nye system er mere effektivt end det gamle.

Notice two things:

1. det replaces den
2. the adjective after er may also change, depending on the noun and adjective form

This is a good reminder that Danish adjectives and articles depend a lot on the noun’s gender and form.